<div class="box">
   <img src="http://tpverstak.ru/wp-content/uploads/2017/05/kitty.jpg" alt="">
</div>

.box {
   position: relative;
   overflow:hidden;
   width:300px;
   height:300px;
}
.box img {
   position: absolute;
   top:50%;
   left:50%;
   -webkit-transform:translate(-50%,-50%);
       -ms-transform:translate(-50%,-50%);
           transform:translate(-50%,-50%);
   width:300px;
   height:300px;
   -o-object-fit:cover;
      object-fit:cover;
}