Community structure is one of most important characteristics of complex networks. The community detection problem based on modularity is NP-hard as a combinatorial optimization problem, which is often solved by heuristic algorithms. Jaya algorithm is a simple and effective meta-heuristic method for solving continuous optimization problems. In this study, the strategy of discreting Jaya algorithm for complex network community discovery is given on the basis of updating the population individuals according to the way Jaya algorithm works, that is, an individual is updated close to the best solution and far away from the worst solution, and thus a discrete Jaya algorithm for complex network community discovery is proposed. Experiments show that the proposed algorithm has the advantages of high resolution and automatic determination of the number of communities compared with the classical algorithms in several real network instances and a class of artificial network instances.