<body>
  <div class="custom-select js-select">
    <i class="custom-select__icon js-icon">
      <img src="http://flaticons.net/icons/Mobile%20Application/Calendar-Date-04.png" alt="" />
    </i>
    <label class="custom-select__label">
      Select age
    </label>
    <div class="custom-select__option-container js-dropdown">
      <div class="custom-select__inner">
        <div class="custom-select__option">
          <label>Option 1</label>
          <input type="checkbox" />
        </div>
        <div class="custom-select__option">
          <label>Option 2</label>
          <input type="checkbox" />
        </div>
        <div class="custom-select__option">
          <label>Option 3</label>
          <input type="checkbox" />
        </div>
        <div class="custom-select__option">
          <label>Option 4</label>
          <input type="checkbox" />
        </div>
      </div>
    </div>
  </div>
</body>
body {
  position: absolute;
  width: 100%;
  min-height: 100%;
  background-color: #ddd9ce;
}

.custom-select {
  position: relative;
  width: 150px;
  padding: 1.5rem;
  margin-right: auto;
  margin-left: auto;
  font-family: sans-serif;
  color: white;
  background-color: #996b33;
  cursor: pointer;
}

.custom-select__icon {
  height: 1rem;
  width: 1rem; 
  vertical-align: middle;
  
  img {
    height: 1rem;
    width: 1rem;
  }
}

.custom-select__label {
  margin-left: 10px;
  vertical-align: middle;
  
  &:before,
  &:after {
    content: '';
    position: absolute;
    top: 50%;
    width: 10px;
    height: 2px;
    background-color: white;
  }
  
  &:before {
    right: 1.5em;
    transform: translate(-25%, -50%) rotate(45deg)
  }
  
  &:after {
    right: 1.5em;
    transform: translate(25%, -50%) rotate(-45deg); 
  }
}

.custom-select__option-container {
  position: absolute;
  top: 100%;
  left: 0;
  margin-top: 10px;
  width: 100%;
  height: auto;
  background-color: white;
  transform: rotateY(180deg);
  transition: transform 295ms ease-in-out;
  backface-visibility: hidden;
  
  &.is-open {
    transform: rotateY(360deg);
  }
}

.custom-select__inner {
  position: relative;
    
  &:before {
    content: '';
    position: absolute;
    bottom: 100%;
    left: 50%;
    width: 0;
    height: 0;
    border-left: 20px solid transparent;
    border-right: 20px solid transparent;
    border-bottom: 20px solid white;
    transform: translateX(-50%);
  }
}

.custom-select__option {
  position: relative;
  display: flex;
  justify-content: space-between;
  align-items: center;
  padding: 10px 1.2em;
  color: lighten(#383b45, 30);
  
  &:after {
    content: '';
    position: absolute;
    top: 100%;
    right: 20px;
    left: 20px;
    height: 1px;
    background-color: lighten(#383b45, 50);
  }
  
  &:last-child:after {
    display: none;
  }
}

input[type=checkbox] {
  appearance: none;
  position: relative;
  width: 20px;
  height: 20px;
  border: 1px solid lighten(#383b45, 50);
}

input[type=checkbox]:checked {
  
  &:after {
    content: '';
    position: absolute;
    top: 50%;
    left: 50%;
    width: 13px;
    height: 7px;
    border: none;
    border-bottom: 3px solid lighten(#383b45, 50);
    border-left: 3px solid lighten(#383b45, 50);
    transform: translate(-50%, -75%) rotate(-45deg);
  }
}
View Compiled
var $select = $('.js-select'),
  $dropdown = $('.js-dropdown'),
  $checkbox = $('input[type=checkbox]'),
  $icon = $('.js-icon'),
  isOpen = false;

var openSelection = function()  {
  $dropdown.addClass('is-open');
  isOpen = true;
}

var closeSelection = function() {
  $dropdown.removeClass('is-open');
  isOpen = false;
}

$checkbox.on('click', function(e) {
  console.log('click');
});

$select.each(function(i, wrap) {
  var $wrap = $(wrap);
  
  $wrap.on('click', function() {
    isOpen ? closeSelection() : openSelection();
  });
});

External CSS

  1. https://cdnjs.cloudflare.com/ajax/libs/select2/4.0.3/css/select2.min.css

External JavaScript

  1. https://code.jquery.com/jquery-2.2.4.min.js
  2. https://cdnjs.cloudflare.com/ajax/libs/velocity/1.2.3/velocity.min.js