Gastrointestinal cancer is becoming increasingly common, which leads to over 3 million deaths every year. No typical symptoms appear in the early stage of gastrointestinal cancer, posing a significant challenge in the diagnosis and treatment of patients with gastrointestinal cancer. Many patients are in the middle and late stages of gastrointestinal cancer when they feel uncomfortable, unfortunately, most of them will die of gastrointestinal cancer. Recently, various artificial intelligence techniques like machine learning based on multi-omics have been presented for cancer diagnosis and treatment in the era of precision medicine. This paper provides a survey on multi-omics-based cancer diagnosis using machine learning with potential application in gastrointestinal cancer. Particularly, we make a comprehensive summary and analysis from the perspective of multi-omics datasets, task types, and multi-omics-based integration methods. Furthermore, this paper points out the remaining challenges of multi-omics-based cancer diagnosis using machine learning and discusses future topics.