<script
src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js">
</script>
<select name="select1" id="select1">
<option value="">Select Country</option>
<option value="india">India</option>
<option value="america">America</option>
</select>


<select name="select2" id="select2" style="display: none;">
<option value="">Select State</option>
<option data-value="india" value="orissa">Orissa</option>
<option data-value="india" value="telangan">Telangan</option>
<option data-value="america" value="america">USA</option>
<option data-value="america" value="america">California</option>
</select>

<select name="select3" id="select3" style="display: none;">
<option value="">Select city</option>
<option data-value="orissa">Nal</option>
<option data-value="orissa">Mir</option>
<option data-value="telangan">Hyd</option>
<option data-value="telangan">Vija</option>
<option data-value="america">KRK</option>
<option data-value="america">MRK</option>
</select>
Script below
<script>
$("#select1").change(function() {
if ($(this).data('options') == undefined) {
$(this).data('options', $('#select2 option').clone());
}
var id = $(this).val();
var options = $(this).data('options').filter('[data-value=' + id + ']');
$('#select2').html(options).show();
});


$("#select2").change(function() {
if ($(this).data('options') == undefined) {
$(this).data('options', $('#select3 option').clone());
}
var id = $(this).val();
var options = $(this).data('options').filter('[data-value=' + id + ']');
$('#select3').html(options).show();
});
</script>