Anti-cancer drug design has been acknowledged as a complicated, expensive, time-consuming, and challenging task. How to reduce the research costs and speed up the development process of anti-cancer drug designs has become a challenging and urgent question for the pharmaceutical industry. Computer-aided drug design methods have played a major role in the development of cancer treatments for over three decades. Recently, artificial intelligence has emerged as a powerful and promising technology for faster, cheaper, and more effective anti-cancer drug designs. This study is a narrative review that reviews a wide range of applications of artificial intelligence-based methods in anti-cancer drug design. We further clarify the fundamental principles of these methods, along with their advantages and disadvantages. Furthermore, we collate a large number of databases, including the omics database, the epigenomics database, the chemical compound database, and drug databases. Other researchers can consider them and adapt them to their own requirements.