With the advancement of modern science and technology, the volume of data generated through human production and daily life has surged. Traditional silicon-based storage media such as hard disks and flash memory are gradually becoming inadequate to meet the growing global data storage demands. Due to its remarkable advantages, such as incredibly high storage density, extremely long-term storage capabilities, and minimal energy consumption, DNA is regarded as the ideal next-generation storage medium. This review primarily focuses on DNA storage technology. It introduces the fundamental theory and workflow, and subsequently provides an overview of the research status regarding data security in DNA storage technology, within the context of conventional data security. This includes aspects like data encryption, data resilience, the detection of bio-cyber attacks and so on. The article also discusses the challenges and emerging trends in data security of DNA storage technology. Through interdisciplinary development, DNA storage technology is expected to resolve the conflict between massive data and limited conventional storage space and can be commercialized in multiple scenarios eventually, all while ensuring broad-spectrum and multi-tier data security.