Hi  Asifpatel,
I have created a sample which full fill your requirement
SQL
CREATE TABLE MultiLine (ID INT IDENTITY,[VALUES] NVARCHAR(MAX))
HTML
<div>
    <asp:TextBox ID="txtMessage" runat="server" TextMode="MultiLine" Rows="5" />
    <asp:Button ID="btnSubmit" Text="Submit" OnClick="Save" runat="server" />
    <br />
    <asp:GridView ID="gvData" runat="server" />
</div>
C#
protected void Save(object sender, EventArgs e)
{
    string replaceValue = txtMessage.Text.Replace(Environment.NewLine, "$");
    string[] values = replaceValue.Split('$');
    foreach (string item in values)
    {
        SaveRecord(item.Trim());
    }
    BindGrid();
}
public void SaveRecord(string value)
{
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand("INSERT INTO MultiLine VALUES(@Value)", con))
        {
            con.Open();
            cmd.Parameters.AddWithValue("@Value", value);
            cmd.ExecuteNonQuery();
            con.Close();
        }
    }
}
public void BindGrid()
{
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand("SELECT * FROM MultiLine", con))
        {
            SqlDataAdapter sda = new SqlDataAdapter(cmd);
            DataTable dt = new DataTable();
            sda.Fill(dt);
            gvData.DataSource = dt;
            gvData.DataBind();
        }
    }
}
VB.Net
Protected Sub Save(sender As Object, e As EventArgs)
	Dim replaceValue As String = txtMessage.Text.Replace(Environment.NewLine, "$")
	Dim values As String() = replaceValue.Split("$"C)
	For Each item As String In values
		SaveRecord(item.Trim())
	Next
	BindGrid()
End Sub
Public Sub SaveRecord(value As String)
	Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
	Using con As New SqlConnection(constr)
		Using cmd As New SqlCommand("INSERT INTO MultiLine VALUES(@Value)", con)
			con.Open()
			cmd.Parameters.AddWithValue("@Value", value)
			cmd.ExecuteNonQuery()
			con.Close()
		End Using
	End Using
End Sub
Public Sub BindGrid()
	Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
	Using con As New SqlConnection(constr)
		Using cmd As New SqlCommand("SELECT * FROM MultiLine", con)
			Dim sda As New SqlDataAdapter(cmd)
			Dim dt As New DataTable()
			sda.Fill(dt)
			gvData.DataSource = dt
			gvData.DataBind()
		End Using
	End Using
End Sub
ScreenShot
