希望能提供在线demo，才能帮你分析问题。

<el-cascader
                            v-model="selected"
                            :options="permissions"
                            :props="{ multiple: true, checkStrictly: true}"
                    ></el-cascader>
data(){
  　selected:["1","1-1"],
 　permissions :[
    {
        value: '1',
        label: '计算机学院',
        children: [
            {
                value: "1-1",
                label: "17级"
            },
        ],
    },
    {
        value:'2',
        label:'陶瓷学院',
        children:[
            {
                value:"2-1",
                label:"17级"
            }
        ]
    }
];　
}

回显示只显示第一级，下一级的选不上
默认只选中　计算机学院

唔，是你的数据有问题，正确是：

data() {
  return {
    selected: [
      ['1'], //计算机学院
      ['1', '1-1'] //计算机学院/17级
    ]
  }
}

可以了，非常感谢

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