效果图：

首先需要安装：

npm install --save @riophae/vue-treeselect

用法看代码注释：

 <template>
 <el-form ref="form"
           :model="searchForm"
           label-width="100px"
           :inline="true"
           :size="$formSize">
    <el-form-item label="区域：">
      <treeselect :append-to-body="true"
                  v-model="searchForm.areaId"
                  :options="areaAllList"
                  :normalizer="normalizer"
                  :show-count="true"
                  placeholder="请选择所属区域" />
    </el-form-item>
 </el-form>
 </template>

<script>
//引入插件
import Treeselect from "@riophae/vue-treeselect";
import "@riophae/vue-treeselect/dist/vue-treeselect.css";

export default {
  //使用组件
  components: { Treeselect },
  data () {
    return {
      areaAllList: [],
      searchForm: {
        areaId: null,//绑定值必须为null,否则输入框中会提示unkonwn
      },
    }
  },
  mounted () {
    this.getAreaAll()
  },
  methods: {
    //转换菜单数据结构
    normalizer (node) {
      if (node.children && !node.children.length) {
        delete node.children;
      }
      return {
        id: node.areaId,
        label: node.areaName,
        children: node.children,
      };
    },
    //调用接口获取select选项数据
    getAreaAll () {
      request({
        url: `/manager/Area/AllAreaTree`,
        method: "get",
      }).then((res) => {
        if (res[SETTING.MANAGER_STATE] === SETTING.MANAGER_SUCCESS_STATE) {
          this.areaAllList = res.data;
        } else {
          this.$message({
            type: "error",
            message: res.message || "操作失败",
          });
        }
      });
    },
  }
}
</script>

<style lang="scss" scoped>
::v-deep .vue-treeselect__control {
  max-width: 215px;
}
</style>