Hi meetsree83,
No there is no other way to validate. You have to use RequiredFieldValidator.
Please refer below sample, In below sample explain about how to use RequiredFieldValidator inside TemplateField.
HTML
<asp:GridView ID="gvCustomers" runat="server" AutoGenerateColumns="false">
    <Columns>
        <asp:BoundField DataField="Id" HeaderText="Id" />
        <asp:BoundField DataField="Name" HeaderText="Name" />
        <asp:TemplateField HeaderText="Country">
            <ItemTemplate>
                <asp:TextBox ID="txtCountry" Text='<%# Eval("Country") %>' runat="server"></asp:TextBox>
                <asp:RequiredFieldValidator ID="rfvCountry" runat="server" ControlToValidate="txtCountry"
                    ErrorMessage="Fill Data" ForeColor="#ff3300"></asp:RequiredFieldValidator>
            </ItemTemplate>
        </asp:TemplateField>
    </Columns>
</asp:GridView>
Namespaces
C#
using System;
using System.Data;
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.AddRange(new DataColumn[3] 
        { 
                        new DataColumn("Id", typeof(int)),
                        new DataColumn("Name", typeof(string)),
                        new DataColumn("Country",typeof(string)) 
        });
        dt.Rows.Add(1, "John Hammond", "United States");
        dt.Rows.Add(2, "Mudassar Khan", "India");
        dt.Rows.Add(3, "Suzanne Mathews", "France");
        dt.Rows.Add(4, "Robert Schidner", null);
        this.gvCustomers.DataSource = dt;
        this.gvCustomers.DataBind();
    }
}
For more details refer below article.
Using ASP.Net RequiredFieldValidator for TextBox inside GridView TemplateField ItemTemplate