mysqlのポートが使われていたので変更している。

docker-compose.yml

version: '3.1'

services:

  ghost-compose:
    image: ghost
    restart: always
    volumes:
      - ./ghost:/var/lib/ghost/content
    ports:
      - 3001:2368
    environment:
      database__client: mysql
      database__connection__host: ghost-db
      database__connection__port: 3303
      database__connection__user: root
      database__connection__password: password
      database__connection__database: ghost

  ghost-db:
    image: mysql
    restart: always
    environment:
      MYSQL_ROOT_PASSWORD: password
      MYSQL_TCP_PORT: 3303
    volumes:
      - ./mysql:/var/lib/mysql
    ports:
      - 3303:3306
    expose:
      - 3303