SOURCE

var vm = new Vue({
        el: '#app',
        data: {
            index: 0
        },
        methods: {
            checkActive(index) {
              this.index = index
            }
        }
    })

<div id="app">
  <div class="nav">
  <p :class="{'active': index == 0}" @click="checkActive(0)">nav1</p>
  <p :class="{'active': index == 1}" @click="checkActive(1)">nav2</p>
  <p :class="{'active': index == 2}" @click="checkActive(2)">nav3</p>
</div>
<a href="http://www.baidu.com">baidu</a>
</div>

.nav{overflow:hidden}
.nav p{float:left;margin-right:10px;cursor: pointer;}
.nav p.active{color:red}