Abstract: The research progress of quantum nonreciprocity was reviewed based on cavity optomechanical system including the introduction of cavity optomechanical system and the concept and application of nonreciprocity in the cavity optomechanical system. The current studies of nonreciprocal transmission in the cavity optomechanical systems were divided into two categories: one is the nonreciprocal transmission in the same frequency domain, such as the transmission between two different optical frequencies, and the other is the nonreciprocal transmission between the two different frequency domains, such as the transmission between optical frequency and microwave frequency. In addition, nonreciprocal devices based on cavity optomechanics, such as isolators, directional amplifiers, circulators and routers, were discussed. Finally, the prospect of the application of nonreciprocity based on cavity optomechanical system in quantum information was prospected.