I have used the below code is working fine but instead of an HTML controller, I have to use the asp.net text box controller.
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet"/>
<style>
input[type="search"]::-webkit-search-cancel-button {
-webkit-appearance: searchfield-cancel-button;
}
</style>
<div class="form-inline">
<input type="search" placeholder="Search..." class="form-control" />
</div>