Edit in JSFiddle

$('textarea').keypress(function (e) {
  // check if user pressed 'Enter'
  if(e.which == 13) 
  {
   // get control object to modify further
   var control = e.target;
          
    // get existing 'Height' of pressed control
   var controlHeight = $(control).height();

   //add some height to existing height of control, I chose 17 as my line-height was 17 for the control 
   $(control).height(controlHeight+17);
  }
});

$('textarea').blur(function (e) {
    
    // Here we get exact number of lines in our TextArea
    var textLines = $(this).val().trim().split(/\r*\n/).length; 

    // Now apply the number Of Lines * line-height to your control. That's all.
    $(this).val($(this).val().trim()).height(textLines*17);
});

<textarea></textarea>