解决办法：

1、用ES6箭头函数，箭头方法可以和父方法共享变量

created () {
    axios.get('http://localhost:3001/todos')
      .then((res) => {
        this.todos = res.data
      })
      .catch((error) => {
        console.log(error)
      })
  }

2、在请求axios外面定义一下 var that=this

created () {
    var that = this
    axios.get('http://localhost:3001/todos')
      .then(function (res) {
        that.todos = res.data
      })
      .catch(function (error) {
        console.log(error)
      })
  }