效果图一：多选
效果图二：选项筛选
最后奉献源码，复制出来直接可用
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>支持搜索选项和多选的下拉框</title>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
</head>
<style>
.dropdown-menu {
overflow-x: visible;
overflow-y: auto;
max-height: 300px;
}
</style>
<body>
<ul class="nav navbar-nav" >
<li class="dropdown" >
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="false">
<b>位置:</b> 
<label id="selectPosition">选择</label><span class="caret"></span>
</a>
<ul id="select_item" class="dropdown-menu" > </ul>
</li>
</ul>
</body>
<script src="http://code.jquery.com/jquery-2.1.4.min.js"></script>
<script type="text/javascript" src="http://libs.baidu.com/bootstrap/3.0.3/js/bootstrap.min.js"></script>
<script>
//设置搜索选项功能
var all_content = ['上面','aaa','cvb','dgf','gdf','dffh','erte','fdg','fghfg','erte','sdfs','gftjhgj']//选项
var select_item_obj = $("#select_item")//下拉框对象
select_item_obj.empty()
select_item_obj.append('<input id="input_search" class="select_search" type="text" class="input-sm" placeholder="搜索">')
for (let j = 0; j < all_content.length; j++) {
select_item_obj.append("<li class='select_item'><a href='#'>" + all_content[j] + "  <span class='glyphicon glyphicon-ok hidden' ></span></a></li>")
}
var input_search_obj = $("#input_search")//搜索框对象
//设置下拉框筛选事件
input_search_obj.on("propertychange input ", function () {
let search_msg = $(this).val()
select_item_obj.children('.select_item').each(function () {
$(this).remove()
})
if (search_msg != '') {
let select_content = []
for (let j = 0; j < all_content.length; j++) {
if (all_content[j].toLowerCase().indexOf(search_msg.toLowerCase()) >= 0) {
select_content.push(all_content[j])
}
}
console.log(select_content)
for (let j = 0; j < select_content.length; j++) {
select_item_obj.append("<li class='select_item'><a href='#'>" + select_content[j] + "  <span class='glyphicon glyphicon-ok hidden' ></span></a></li>")
}
} else {
for (let j = 0; j < all_content.length; j++) {
select_item_obj.append("<li class='select_item'><a href='#'>" + all_content[j] + "  <span class='glyphicon glyphicon-ok hidden' ></span></a></li>")
}
}
//将下拉框的值设置为显示的值，由于下拉框处于动态变化，所以必须放在变化最后的位置，才能保证全部的下拉框绑定事件
$('ul.dropdown-menu li.select_item').on('click', function (e) {
var ul_obj = $(this).parent()
var glyphicon_obj = $(this).children('a').children('span')
var glyphicon_class = glyphicon_obj.attr('class')
if (glyphicon_class == 'glyphicon glyphicon-ok') {
glyphicon_obj.attr('class', 'glyphicon glyphicon-ok hidden')
} else {
glyphicon_obj.attr('class', 'glyphicon glyphicon-ok')
}
var label_val = ''
ul_obj.find('li').each(function () {
var select_falg = $(this).children('a').children('span')
var now_obj = $(this)
if (select_falg.attr('class') == 'glyphicon glyphicon-ok') {
label_val += $.trim(now_obj.text()) + ','
}
})
console.log(label_val)
if (label_val == '') {
label_val = '选择'
}
$(this).parent().prev().children('label').text($.trim(label_val))
$(this).parent().prev().children('label').val($.trim(label_val))
e.stopPropagation();
})
})
//将下拉框的值设置为显示的值，由于下拉框处于动态变化，所以必须放在变化最后的位置，才能保证全部的下拉框绑定事件
$('ul.dropdown-menu li.select_item').on('click', function (e) {
var ul_obj = $(this).parent()
var glyphicon_obj = $(this).children('a').children('span')
var glyphicon_class = glyphicon_obj.attr('class')
if(glyphicon_class=='glyphicon glyphicon-ok'){
glyphicon_obj.attr('class','glyphicon glyphicon-ok hidden') }else{
glyphicon_obj.attr('class','glyphicon glyphicon-ok')
}
var label_val = ''
ul_obj.find('li').each(function () {
var select_falg = $(this).children('a').children('span')
var now_obj = $(this)
if(select_falg.attr('class')=='glyphicon glyphicon-ok'){
label_val += $.trim(now_obj.text())+','
}
})
console.log(label_val)
if(label_val==''){label_val='选择'}
$(this).parent().prev().children('label').text($.trim(label_val))
$(this).parent().prev().children('label').val($.trim(label_val))
e.stopPropagation();
})
//阻断li的点击事件
$(".select_search").on('click', function (e) {
e.stopPropagation();
});
</script>
</html>