I got some select tag as follows:
DEMO
What you are asking for is the default functionality of drop-down-list.
if you want to search the drop-down-list you can try this plugin.
jQuery Searchable DropDown Plugin Demo
DEMO - with your code
$('#fruits').searchable();
you can also try DEMO
I think this is the default action of drop down(select control). You have to do zero effort to achieve it.
try this JSbin
.. there is a select box and when user first presses g
on the keyboard grapes is selected
and on second ginger is selected
http://jsbin.com/UYeZaPA/1/edit
Well, If you want to add Auto Complete functionality to your html select element then there is nothing better than selectize.js
All you need to do is either include its css and js file in your project or you can use cdns.
Go to Selectize website here