Edit in JSFiddle

  const vm = new Vue({
    el: "#app",
    data: {a: ""},
  })
<div id="app">
  <div class="form-horizontal">
    <div class="form-group">
      <label class="col-md-2 control-label">本文</label>
      <div class="col-md-10">
        <textarea class="form-control" v-model="a" :rows="a.split(/\n/).length"></textarea>
      </div>
    </div>
  </div>
</div>