Hi EmadKhan,
Refer the below sample.
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title></title>
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<link rel="stylesheet" type="text/css" href="http://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.0.3/css/bootstrap.min.css" />
<script type="text/javascript" src="http://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.0.3/js/bootstrap.min.js"></script>
<link rel="stylesheet" type="text/css" href="http://cdn.rawgit.com/davidstutz/bootstrap-multiselect/master/dist/css/bootstrap-multiselect.css" />
<script type="text/javascript" src="http://cdn.rawgit.com/davidstutz/bootstrap-multiselect/master/dist/js/bootstrap-multiselect.js"></script>
<script type="text/javascript">
$(function () {
$("[id*=DailyLogWeekRangeDrp] option[value='-1']").remove();
$('[id*=DailyLogWeekRangeDrp]').multiselect();
});
</script>
</head>
<body>
<form id="form1" runat="server">
<div>
<select size="4" name="DailyLogWeekRangeDrp" multiple="multiple" id="DailyLogWeekRangeDrp">
<option value="-1">ALL DATES: 23-NOV-2015 TO 26-MAR-2017</option>
<option value="2">WEEK 1: 23-NOV-2015 TO 29-NOV-2015</option>
<option value="3">WEEK 2: 30-NOV-2015 TO 06-DEC-2015</option>
<option value="4">WEEK 3: 07-DEC-2015 TO 13-DEC-2015</option>
<option value="5">WEEK 4: 14-DEC-2015 TO 20-DEC-2015</option>
<option value="6">WEEK 5: 21-DEC-2015 TO 27-DEC-2015</option>
</select>
</div>
</form>
</body>
</html>
Demo
Aspx ListBox
<asp:ListBox SelectionMode="Multiple" ID="DailyLogWeekRangeDrp" runat="server" Width="100%">
<asp:ListItem Text="ALL DATES: 23-NOV-2015 TO 26-MAR-2017" Value="-1" />
<asp:ListItem Text="WEEK 1: 23-NOV-2015 TO 29-NOV-2015" Value="2" />
<asp:ListItem Text="WEEK 2: 30-NOV-2015 TO 06-DEC-2015" Value="3" />
<asp:ListItem Text="WEEK 3: 07-DEC-2015 TO 13-DEC-2015" Value="4" />
<asp:ListItem Text="WEEK 4: 14-DEC-2015 TO 20-DEC-2015" Value="5" />
<asp:ListItem Text="WEEK 5: 21-DEC-2015 TO 27-DEC-2015" Value="6" />
</asp:ListBox>
