Edit in JSFiddle

$(window).scroll(function(){
    if($(document).scrollTop() > 0) {
        $('.header_wrap').addClass('scrolled');
    } else {
        $('.header_wrap').removeClass('scrolled');
    }
});

<div class="header_wrap">
  <div class="header">
    <h2 class="logo">
      LOGO
    </h2>
  </div>
</div>

<div id="container">
  <p>contents line 1</p>
  <p>contents line 2</p>
  <p>contents line 3</p>
  <p>contents line 4</p>
  <p>contents line 5</p>
  <p>contents line 6</p>
  <p>contents line 7</p>
  <p>contents line 8</p>
  <p>contents line 9</p>
  <p>contents line 10</p>
  <p>contents line 11</p>
  <p>contents line 12</p>
  <p>contents line 13</p>
  <p>contents line 14</p>
  <p>contents line 15</p>
  <p>contents line 16</p>
  <p>contents line 17</p>
  <p>contents line 18</p>
  <p>contents line 19</p>
  <p>contents line 20</p>
</div>

body {
  margin: 0;
  background-color: #b8b8dc;
}

.header_wrap {
  height: 120px;
}
.header_wrap .header {
  position: fixed;
  top: 0;
  width: 100%;
  height: 120px;
  background: parent;
  
  transition: 0.5s;
  -webkit-transition: 0.5s;
  -moz-transition: 0.5s;  
}
.header_wrap .header .logo{
  margin: 0;
  padding: 0 30px;
  font-size: 40px;
  line-height: 120px;
  
  transition: 0.5s;
  -webkit-transition: 0.5s;
  -moz-transition: 0.5s;
}


.header_wrap.scrolled {
  height: 60px;
}
.header_wrap.scrolled .header {
  height: 60px;
  background-color: #ffffff;
}
.header_wrap.scrolled .header .logo{
  font-size: 20px;
  line-height: 60px;
}