Edit in JSFiddle

<select>
    <option value="1">options 1</option>
    <option value="2">options 2</option>
    <option value="3">options 3</option>
</select>
select {
    -webkit-appearance: none;
    -moz-appearance: none;
    appearance: none;
    border: 1px solid #555;
    width: 80%;
    height: 34px;
    background: #eee url(http://www.stackoverflow.com/favicon.ico) right center no-repeat;
}

select::-ms-expand { /* for IE 11 */
    display: none;
}