Is it possible to create a custom dropdown box using javascriit and css.
for which i need to place a background-image for dropdown box using javascript
If ye
This might be overkill; but SproutCore gives you input elements composed from images instead of from native HTML elements. There are probably other frameworks that do similar things.
The basic idea is to create a div or something, as CrazyJugglerDrummer suggests, and put click handlers on it. The handlers set up animation to mimic a select element. And when one of your pseudo-select items is selected, you use JavaScript to send that value to an actual select or input element that is hidden.