The growing incorporation of artificial intelligence (AI) into medical device software offers substantial prospects and regulatory hurdles. As AI software as a medical device (AI-SaMD) continues to advance, ensuring its safety, effectiveness, and security is paramount. Nevertheless, the regulatory environment needs more cohesion, with various regions implementing diverse strategies. This paper underscores the necessity for globally harmonized AI-SaMD regulations by examining key regulatory frameworks from the United States, the European Union, China, and Australia. The article also explores crucial elements for harmonization, including algorithm transparency, risk management, data security, and clinical evaluation. Furthermore, the paper advocates for implementing international standards and global data security protocols, emphasizing the significance of cross-border cooperation to ensure the worldwide safety and efficacy of AI-SaMD.