<div id="vueContainer">
    <div>
      <input type='checkbox' class='input-checkbox' :checked="fruitIds.length === fruits.length" @click='checkedAll()'>全选
      <div v-for='(fruit, index) in fruits' :key="index">
          <!--判断fruitIds是否包含当前fruit，fruitIds.indexOf(fruit.fruitId)返回包含fruit的下标, 若不包含则返回-1-->
         <input type='checkbox' :checked="fruitIds.indexOf(fruit.fruitId) > -1" name='checkboxinput' class='input-checkbox' @click='checkedOne(fruit.fruitId)'>
      	{{fruit.value}}
      </div>
      <!--默认删除按钮不能点击, 当选中某一checkbox时可以删除-->
      <button :disabled="!fruitIds.length>0" value="Delete" @click="deleteFruits()">Delete</button>
    </div>
</div>

<script>
    var vue = new Vue({
        el: "#vueContainer",
        data: {
            fruits:[{
                    fruitId:'1',
                    value:'苹果'
                },{
                    fruitId:'2',
                    value:'荔枝'
                },{
                    fruitId:'3',
                    value:'香蕉'
                },{
                    fruitId:'4',
                    value:'火龙果'
                }
            ],
            fruitIds:['1','3','4'],
            isCheckedAll: false
        },
        methods:{
            checkedOne (fruitId) {
                let idIndex = this.fruitIds.indexOf(fruitId)
                if (idIndex >= 0) {
                    // 如果已经包含了该id, 则去除(单选按钮由选中变为非选中状态)
                    this.fruitIds.splice(idIndex, 1)
                } else {
                    // 选中该checkbox
                    this.fruitIds.push(fruitId)
                }
            },
            checkedAll () {
                this.isCheckedAll = !this.isCheckedAll
                if (this.isCheckedAll) {
                    // 全选时
                    this.fruitIds = []
                    var _that = this
                    // 此写法 其实就是异步函数 this 的指向问题，传入一个this参数
//                  this.fruits.forEach(function (fruit) {
//                  	console.log(fruit)
//                      this.fruitIds.push(fruit.fruitId)
//                  },this)
					this.fruits.forEach((val,index) =>{
						this.fruitIds.push(val.fruitId)
					})
                } else {
                    this.fruitIds = []
                }
            },
            deleteFruits () {
            	var newDate = [];
				this.fruits.forEach((val,index) => {
					if (!(this.fruitIds.indexOf(val.fruitId) > -1)) {
						newDate.push(val)
					}
					
				})
				this.fruits = newDate;
				this.fruitIds = [];
//				var arr = [];
//		        var len = this.fruits.length;
//		        for(var i=0;i<len;i++){
//		            if(this.fruitIds.indexOf(this.fruits[i].fruitId)>=0){
//		                console.log(this.fruitIds.indexOf(i));
//		            }else {
//		                console.log(this.fruits[i]);
//		                arr.push(this.fruits[i]);
//		            }
//		        }
//		        this.fruits = arr;
//		        this.fruitIds = [];
    		}
        }
    });
</script>

参考了博客 https://www.cnblogs.com/smileself/p/checkAll.html 

并在其基础上新增了删除操作，如有问题欢迎道友留言