Edge computing can reduce service latency and save backhaul bandwidth by completing services at network edges, providing support for diverse computation-intensive and delaysensitive services. However, it is not practical to support all services at edge nodes due to the limited network resources. The decision that which services can be provided locally and which services should been offloaded to cloud significantly impacts the user experience. Cloud-edge computing offloading becomes an important issue in edge computing. In this paper, we take the fairness into the optimization objective of computing offloading problem, and consider both computing capacity and storage space as problem constraints. The problem is formulated as a long-term average optimization problem to maximize the αfair utility function of saved time, and further translated as a Markov decision process. As the optimization problem with fairness guarantee and huge action space, we cannot solve it with traditional methods. Therefore, an innovative multi-update deep reinforcement learning algorithm is proposed which can optimize the objective with α-fair utility function and reduce dramatically the size of action space. We also prove the convergence of our algorithm theoretically. To our best knowledge, the longterm average optimization of computing offloading with fairness guarantee is rarely seen in literature. Extensive simulation experiments show that our algorithm can converge quickly and has better performance in terms of service delay and fairness.