要解决apollo-server-express的CORS问题，可以按照以下步骤进行操作：

1. 安装依赖库：cors和apollo-server-express

npm install cors apollo-server-express

2. 在你的代码中，引入cors和apollo-server-express：

const express = require('express');
const { ApolloServer, gql } = require('apollo-server-express');
const cors = require('cors');

3. 创建一个Express应用程序并启用CORS：

const app = express();
app.use(cors());

4. 创建GraphQL模式和解析器：

const typeDefs = gql`
  type Query {
    hello: String
  }
`;

const resolvers = {
  Query: {
    hello: () => 'Hello, world!'
  }
};

5. 创建Apollo服务器并将其连接到Express应用程序：

const server = new ApolloServer({ typeDefs, resolvers });
server.applyMiddleware({ app });

完整示例代码如下：

const express = require('express');
const { ApolloServer, gql } = require('apollo-server-express');
const cors = require('cors');

const app = express();
app.use(cors());

const typeDefs = gql`
  type Query {
    hello: String
  }
`;

const resolvers = {
  Query: {
    hello: () => 'Hello, world!'
  }
};

const server = new ApolloServer({ typeDefs, resolvers });
server.applyMiddleware({ app });

app.listen({ port: 4000 }, () =>
  console.log('Server is running at http://localhost:4000' + server.graphqlPath)
);

通过上述步骤，你的apollo-server-express应用程序将启用CORS，并可以处理跨域请求。