.router-link-active{
 background: rgba(255,255,255,0.8);
 color: gray;
 }

<template>
 <nav>
  <ul>
  <li>
   <router-link to="/" exact>博客</router-link>
   <router-link to="/AddBlog" exact>写博客</router-link>
  </li>
  </ul>
 </nav>
</template>
 
<script>
 export default {
  name: "bolgheader"
 }
</script>
 
<style scoped>
 ul{
 list-style-type: none;
 text-align: center;
 margin:0;
 }
 li{
 display: inline-block;
 margin:0 10px;
 }
 a{
 color:rgb(102, 119, 204);
 text-decoration: none;
 padding:12px;
 border-radius: 5px;
 font-size:20px;
 }
 nav{
 background: #eee;
 padding: 30px 0;
 margin-bottom: 40px;
 }
 .router-link-active{
 background: rgba(255,255,255,0.8);
 color: gray;
 }
</style>