*{margin:0;padding:0;}
 /*登陆按钮*/
 #app{
 width:140px;
 height:36px;
 margin:10px auto;
 }
 #login,#login a{
 width: 200px;
 height: 38px;
 line-height:38px;
 text-align: center;
 text-decoration: none;
 font-size: 24px; 
 color: #000;
 }

 /*登陆框*/
 #login-box{
 padding: 20px;
 display:none;
 width:350px;
 height: 150px;
 background: #eeeeee;
 border-radius: 5px;
 position: absolute;
 margin-left: -80px;
 margin-top: 150px;
 }
 #login-box>form{
 text-align: center;
 }
 #login-box label{
 display: block;
 font-size: 20px;
 margin: 10px 0 0 0;
 }
 #login-box label input{
 width:200px;
 height: 30px;
 }
 #login-box button{
 width:200px;
 height: 30px;
 margin:10px 0 0 0;
 width:90px;
 border-radius: 5px;
 }
 #close{
 font-size:18px;
 position: absolute;
 top:0;
 right: 5px;
 cursor: pointer;
 }
 /*背景*/
 #back{
 position:absolute;
 left:0;
 top:0;
 width:100%;
 height:100%;
 background: #000;
 opacity: 0.5;
}

<div id="app">
 <!--登陆按钮-->
 <h3 id="login" v-if="isLogin==true">欢迎您 | <a href="javascript:;" @click="logout">注销</a></h3>
 <h3 id="login" v-else><a href="javascript:;" @click="login1">登录</a> | 注册</h3>

 <!--登陆框 -->
 <div id="login-box" :style="log==0">
 <form action="">
 <label>用&nbsp;&nbsp;&nbsp;&nbsp;户:
  <input v-model="uname" type="text" placeholder="请输入用户名...">
 </label>
 <label>密&nbsp;&nbsp;&nbsp;&nbsp;码:
  <input v-model="upwd" type="password" placeholder="请输入密码...">
 </label>
 <button type="button" @click="login2">登录</button>
 <p id="close" @click="close">×</p>
 </form>
 </div>
 
 <!--背景半透明处理-->
 <div id="back" :style="log==0"></div>
</div>

new Vue({
 el:"#app",
 data:{
 isLogin:false,
 log:0,
 uname:"",
 upwd:""
 },
 methods:{
 login1(){
 this.log=1;
 },
 login2(){
 if(this.uname=="hahaha"&&this.upwd=="123456"){
 this.log=0;
 this.isLogin=true;
 }else{
 alert("用户名或密码不正确！");
 }
 },
 close(){
 this.log=0;
 //清空input中的内容
 this.uname="";
 this.upwd="";
 },
 logout(){
 this.isLogin=false;
 this.uname="";
 this.upwd="";
 }
 }
})