Hi  kana250688,
Refer below example.
Namespaces
C#
using System.Data;
VB.Net
Imports System.Data
Code
C#
private void Form1_Load(object sender, EventArgs e)
{
    //Hide the last blank line.
    dataGridView1.AllowUserToAddRows = false;
    //Clear Columns.
    dataGridView1.Columns.Clear();
    //Add Columns.
    DataGridViewColumn customerId = new DataGridViewTextBoxColumn();
    customerId.Name = "CustomerId";
    customerId.HeaderText = "CustomerId Id";
    customerId.DataPropertyName = "CustomerId";
    customerId.Width = 100;
    dataGridView1.Columns.Insert(0, customerId);
    DataGridViewColumn name = new DataGridViewTextBoxColumn();
    name.HeaderText = "Name";
    name.Name = "Name";
    name.DataPropertyName = "Name";
    name.Width = 100;
    dataGridView1.Columns.Insert(1, name);
    DataGridViewColumn country = new DataGridViewTextBoxColumn();
    country.Name = "Country";
    country.HeaderText = "Country";
    country.DataPropertyName = "Country";
    country.Width = 100;
    dataGridView1.Columns.Insert(2, country);
    //Bind the DataGridView.
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[3] {
        new DataColumn("CustomerId"),
        new DataColumn("Name"),
        new DataColumn("Country") });
    dt.Rows.Add(1, "John Hammond", "United States");
    dt.Rows.Add(0, "", "");
    dt.Rows.Add(2, "Mudassar Khan", "India");
    dt.Rows.Add(0, "", "");
    dt.Rows.Add(3, "Suzanne Mathews", "France");
    dt.Rows.Add(0, "", "");
    dt.Rows.Add(4, "Robert Schidner", "Russia");
    dt.Rows.Add(0, "", "");
    dataGridView1.DataSource = dt;
}
private void btnDelete_Click(object sender, EventArgs e)
{
    if (dataGridView1.SelectedRows.Count > 0)
    {
        foreach (DataGridViewRow row in dataGridView1.SelectedRows)
        {
            if (this.CheckIfEmpty(row))
            {
                dataGridView1.Rows.RemoveAt(row.Index);
            }
        }
    }
    else
    {
        MessageBox.Show("Please select a row.");
    }
}
private bool CheckIfEmpty(DataGridViewRow row)
{
    for (int i = 0; i <= row.Cells.Count - 1; i++)
    {
        if (row.Cells[i].Value == null || row.Cells[i].Value == DBNull.Value 
            || string.IsNullOrEmpty(row.Cells[i].Value.ToString())
            || row.Cells[i].Value.ToString() == "0")
        {
            return true;
        }
    }
    return false;
}
VB.Net
Private Sub Form1_Load(sender As System.Object, e As System.EventArgs) Handles MyBase.Load
    'Hide the last blank line.
    dataGridView1.AllowUserToAddRows = False
    'Clear Columns.
    dataGridView1.Columns.Clear()
    'Add Columns.
    Dim customerId As DataGridViewColumn = New DataGridViewTextBoxColumn()
    customerId.Name = "CustomerId"
    customerId.HeaderText = "CustomerId Id"
    customerId.DataPropertyName = "CustomerId"
    customerId.Width = 100
    dataGridView1.Columns.Insert(0, customerId)
    Dim name As DataGridViewColumn = New DataGridViewTextBoxColumn()
    name.HeaderText = "Name"
    name.Name = "Name"
    name.DataPropertyName = "Name"
    name.Width = 100
    dataGridView1.Columns.Insert(1, name)
    Dim country As DataGridViewColumn = New DataGridViewTextBoxColumn()
    country.Name = "Country"
    country.HeaderText = "Country"
    country.DataPropertyName = "Country"
    country.Width = 100
    dataGridView1.Columns.Insert(2, country)
    'Bind the DataGridView.
    Dim dt As DataTable = New DataTable()
    dt.Columns.AddRange(New DataColumn(2) {New DataColumn("CustomerId"), New DataColumn("Name"), New DataColumn("Country")})
    dt.Rows.Add(1, "John Hammond", "United States")
    dt.Rows.Add(0, "", "")
    dt.Rows.Add(2, "Mudassar Khan", "India")
    dt.Rows.Add(0, "", "")
    dt.Rows.Add(3, "Suzanne Mathews", "France")
    dt.Rows.Add(0, "", "")
    dt.Rows.Add(4, "Robert Schidner", "Russia")
    dt.Rows.Add(0, "", "")
    dataGridView1.DataSource = dt
End Sub
Private Sub btnDelete_Click(ByVal sender As Object, ByVal e As EventArgs) Handles btnDelete.Click
    If dataGridView1.SelectedRows.Count > 0 Then
        For Each row As DataGridViewRow In dataGridView1.SelectedRows
            If Me.CheckIfEmpty(row) Then
                dataGridView1.Rows.RemoveAt(row.Index)
            End If
        Next
    Else
        MessageBox.Show("Please select a row.")
    End If
End Sub
Private Function CheckIfEmpty(ByVal row As DataGridViewRow) As Boolean
    For i As Integer = 0 To row.Cells.Count - 1
        If row.Cells(i).Value Is Nothing OrElse IsDBNull(row.Cells(i).Value) _
            OrElse String.IsNullOrEmpty(row.Cells(i).Value.ToString()) _
            OrElse row.Cells(i).Value.ToString() = "0" Then
            Return True
        End If
    Next
    Return False
End Function
Screenshot
