ANSHENG operating system is a secure operating system with high security level based on Linux, which is independently developed with the security kernel, security framework and security models. In this paper, the approaches to analyzing covert channels in the underlying system are summarized, and it is the first time that the covert-channel-analysis results on a secure operating system based on Linux kernel have ever been reported. Some new covert channels have been found by the novel backward tracking approach. For the identified covert channels, accurate bandwidth computation and appropriate covert-channel handling have been performed.