<div class="wrapper">
  <div class="title">
    Custom Select Box
  </div>
  <div class="select_wrap">
      <ul class="default_option">
          <li>
              <div class="option pizza">
                <div class="icon"></div>
                <p>Pizzas</p>
              </div>
          </li>
      </ul>
      <ul class="select_ul">
          <li>
              <div class="option pizza">
                <div class="icon"></div>
                <p>Pizzas</p>
              </div>
          </li>
          <li>
              <div class="option burger">
                <div class="icon"></div>
                <p>Burget</p>
              </div>  
          </li>
          <li>
              <div class="option ice">
                <div class="icon"></div>
                <p>Ice Cream</p>
              </div>  
          </li>
          <li>
            <div class="option fries">
                <div class="icon"></div>
                <p>Fried Potatoes</p>
              </div>
          </li>
      </ul>
  </div>
  
</div>
@import url('https://fonts.googleapis.com/css?family=Montserrat:400,700&display=swap');

*{
  margin: 0;
  padding: 0;
  box-sizing: border-box;
  list-style: none;
  font-family: 'Montserrat', sans-serif;
}

body{
  background: #fdc75b;
  color: #555555;
}

.wrapper{
  position: absolute;
  top: 35%;
  left: 50%;
  transform: translate(-50%,-50%);
}

.wrapper .title{
  font-weight: 700;
  font-size: 24px;
  color: #fff;
}

.select_wrap{
  width: 225px;
  margin: 15px auto;
  position: relative;
  user-select: none;
}

.select_wrap .default_option{
  background: #fff;
  border-radius: 5px;
  position: relative;
  cursor: pointer;
}

.select_wrap .default_option li{
    padding: 10px 20px;
}

.select_wrap .default_option:before{
    content: "";
    position: absolute;
    top: 18px;
    right: 18px;
    width: 6px;
    height: 6px;
    border: 2px solid;
    border-color: transparent transparent #555555 #555555;
    transform: rotate(-45deg);
}

.select_wrap .select_ul{
  position: absolute;
  top: 55px;
  left: 0;
  width: 100%;
  background: #fff;
  border-radius: 5px;
  display: none;
}

.select_wrap .select_ul li{
  padding: 10px 20px;
  cursor: pointer;
}

.select_wrap .select_ul li:first-child:hover{
  border-top-left-radius: 5px;
  border-top-right-radius: 5px;
}

.select_wrap .select_ul li:last-child:hover{
  border-bottom-left-radius: 5px;
  border-bottom-right-radius: 5px;
}

.select_wrap .select_ul li:hover{
  background: #fff4dd;
}

.select_wrap .option{
  display: flex;
  align-items: center;
}

.select_wrap .option .icon{
  background: url('https://i.imgur.com/oEZu0sK.png') no-repeat 0 0;
	width: 32px;
	height: 32px;
  margin-right: 15px;
}

.select_wrap .option.pizza .icon{
  background-position: 0 0;
}

.select_wrap .option.burger .icon{
  background-position:  0 -35px;
}

.select_wrap .option.ice .icon{
  background-position: 0 -72px;
}

.select_wrap .option.fries .icon{
 background-position: 0 -111px;
  width: 25px;
}

.select_wrap.active .select_ul{
  display: block;
}

.select_wrap.active .default_option:before{
  top: 25px;
  transform: rotate(-225deg);
}
$(".default_option").click(function(){
  $(this).parent().toggleClass("active");
})

$(".select_ul li").click(function(){
  var currentele = $(this).html();
  $(".default_option li").html(currentele);
  $(this).parents(".select_wrap").removeClass("active");
})

External CSS

This Pen doesn't use any external CSS resources.

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js