Complex limited-memory BFGS (CL-BFGS) algorithm can be efficiently applied to solve unconstrained optimization problems in complex domain. However, its performance is seriously affected by memory size. In this paper, to deal with the selection problem of memory size, an improved CL-BFGS algorithm with hybrid search directions is proposed. The candidate set of memory size is divided into several parts by the sliding window method and a group of hybrid directions are constructed by considering the elements of each subset as potential memory sizes. Then the hybrid direction achieving the minimum value of objective function is taken as the actual search direction at the current iteration. The advantage of the strategy of hybrid search direction is to strengthen the usage of the latest curvature information and facilitate the choice of memory size such that the performance of the CL-BFGS algorithm is improved. The proposed CL-BFGS algorithm is then applied for the efficient learning of multi-layer feedforward complex-valued neural networks. Finally, experiments are conducted on the tasks of pattern recognition, nonlinear channel equalization and complex function approximation to verify that the proposed algorithm has better performance than some existing ones.