Sir,
I want to click "Google Search" button of google.com in Internet Explorer api through C# code.Is it possible?

Are you referring to web browser (IE) control in Windows Form?
Yes it is possible.

webBrowser.Navigate("http://www.google.com");

In Web Browser DocumentCompleted event,

HtmlElement textElement = webBrowser.Document.All.GetElementsByName("q")[0];
textElement.SetAttribute("value", "your text to search");
HtmlElement btnElement = webBrowser.Document.All.GetElementsByName("btnG")[0];
btnElement.InvokeMember("click");