Hi
I have created a sample which full fill your requirement you need to modify the code according to your need.
HTML
<div>
    <br />
    Country:-
    <asp:TextBox ID="txtCountry" runat="server" TextMode="MultiLine" Rows="10"></asp:TextBox>
    <br />
    <asp:Button ID="btnSearch" Text="Search" OnClick="Search" runat="server" />
    <br />
    <br />
    <asp:GridView ID="gvCustomers" runat="server" />
</div>
C#
protected void Search(object sender, EventArgs e)
{
    string constring = ConfigurationManager.ConnectionStrings["constr"].ToString();
    string countryName = txtCountry.Text.Replace(Environment.NewLine, "#");
    string[] countryNames = countryName.Split('#');
    string query = "SELECT CustomerID,CompanyName,ContactName,Country FROM Customers ";
    string whereCondition = "WHERE ";
    foreach (string name in countryNames)
    {
        whereCondition += "Country LIKE '%" + name + "%' OR ";
    }
    query += whereCondition.Substring(0, whereCondition.LastIndexOf("OR"));
    using (SqlConnection con = new SqlConnection(constring))
    {
        using (SqlCommand cmd = new SqlCommand(query, con))
        {
            DataTable dt = new DataTable();
            SqlDataAdapter sda = new SqlDataAdapter(cmd);
            sda.Fill(dt);
            gvCustomers.DataSource = dt;
            gvCustomers.DataBind();
        }
    }
}
VB.Net
Protected Sub Search(sender As Object, e As EventArgs)
	Dim constring As String = ConfigurationManager.ConnectionStrings("constr").ToString()
	Dim countryName As String = txtCountry.Text.Replace(Environment.NewLine, "#")
	Dim countryNames As String() = countryName.Split("#"C)
	Dim query As String = "SELECT CustomerID,CompanyName,ContactName,Country FROM Customers "
	Dim whereCondition As String = "WHERE "
	For Each name As String In countryNames
		whereCondition += (Convert.ToString("Country LIKE '%") & name) + "%' OR "
	Next
	query += whereCondition.Substring(0, whereCondition.LastIndexOf("OR"))
	Using con As New SqlConnection(constring)
		Using cmd As New SqlCommand(query, con)
			Dim dt As New DataTable()
			Dim sda As New SqlDataAdapter(cmd)
			sda.Fill(dt)
			gvCustomers.DataSource = dt
			gvCustomers.DataBind()
		End Using
	End Using
End Sub
ScreenShot
