Add new row to GridView on each button-Click

Try this:
This example shows how to generate a Row in GridView with TextBoxes when clicking a Button.
Aspx page:

<asp:gridview ID="Gridview1" runat="server" ShowFooter="true" AutoGenerateColumns="false">
        <Columns>
        <asp:BoundField DataField="RowNumber" HeaderText="Row Number" />
        <asp:TemplateField HeaderText="Header 1">
            <ItemTemplate>
                <asp:TextBox ID="TextBox1" runat="server"></asp:TextBox>
            </ItemTemplate>
        </asp:TemplateField>
        <asp:TemplateField HeaderText="Header 2">
            <ItemTemplate>
                <asp:TextBox ID="TextBox2" runat="server"></asp:TextBox>
            </ItemTemplate>
        </asp:TemplateField>
        <asp:TemplateField HeaderText="Header 3">
            <ItemTemplate>
                 <asp:TextBox ID="TextBox3" runat="server"></asp:TextBox>
            </ItemTemplate>
            <FooterStyle HorizontalAlign="Right" />
            <FooterTemplate>
             <asp:Button ID="ButtonAdd" runat="server" Text="Add New Row" />
            </FooterTemplate>
        </asp:TemplateField>
        </Columns>
</asp:gridview>

Code behind:

private void SetInitialRow()
    {
        DataTable dt = new DataTable();
        DataRow dr = null;
        dt.Columns.Add(new DataColumn("RowNumber", typeof(string)));
        dt.Columns.Add(new DataColumn("Column1", typeof(string)));
        dt.Columns.Add(new DataColumn("Column2", typeof(string)));
        dt.Columns.Add(new DataColumn("Column3", typeof(string)));
        dr = dt.NewRow();
        dr["RowNumber"] = 1;
        dr["Column1"] = string.Empty;
        dr["Column2"] = string.Empty;
        dr["Column3"] = string.Empty;
        dt.Rows.Add(dr);
        //dr = dt.NewRow();
 
        //Store the DataTable in ViewState
        ViewState["CurrentTable"] = dt;
 
        Gridview1.DataSource = dt;
        Gridview1.DataBind();
    }

Page load:

protected void Page_Load(object sender, EventArgs e)
    {
        if (!Page.IsPostBack)
        {
            SetInitialRow(); 
        }
    }

[EDIT]
For more have look on following links:
Adding Dynamic Rows in ASP.NET GridView Control with TextBoxes and with Delete functionality[^]
Save and Retrieve Dynamic TextBox values in GridView to SQL Server Database[^]
ADDING DYNAMIC ROWS IN GRIDVIEW WITH TEXTBOXES[^]

Hope it helps!