The development of the Internet of things provides a great opportunity for the development of all walks of life, but it also brings many risks in the process, of which the most important thing is the protection of computer network information security. Digital art museums play a great role in viewing, education, and other functions. This article is aimed at analyzing the computer network information security protection problems faced by digital art museums. Analyze the application of the digital art gallery in the computer Internet of things, and combine the different aspects involved in the two parts to carry out experimental analysis and comparison. The difference between the various subjects of the digital art gallery, such as exhibits, writers, and visitors, is to maintain the security of Internet computer information. Introduce the application. The results show that compared with that of fog computing technology and that of edge computing technology, the performance of the Internet of things is generally better, with faster data processing speed, shorter processing time, higher quality, and stronger scalability. But at the same time, it is also facing greater computer network security threats. According to statistics, 83.3% of consumers worry about its usability but people are more concerned about its safety performance. Nearly 87.5% of consumers worry about whether their information will be leaked. When cloud computing technology is applied to digital art museums, how to protect computer network information security is particularly important. Based on the traditional firewall, this paper designs a hybrid firewall, which can better solve the problem of computer network information security.