A new complex neuro-fuzzy self-learning approach to the problem of function approximation is proposed, where complex fuzzy sets are used to design a complex neuro-fuzzy system as the function approximator. Particle swarm optimization (PSO) algorithm and recursive least square estimator (RLSE) algorithm are used in hybrid way to adjust the free parameters of the proposed complex neuro-fuzzy systems (CNFS). The hybrid PSO-RLSE learning method is used for the CNFS parameters to converge efficiently and quickly to optimal or near-optimal solution. From the experimental results, the proposed CNFS shows better performance than the traditional neuro-fuzzy system (NFS) that is designed with regular fuzzy sets. Moreover, the PSO-RLSE hybrid learning method for the CNFS improves the rate of learning convergence, and shows better performance in accuracy. Three benchmark functions are used. With the performance comparisons shown in the paper, excellent performance by the proposed approach has been observed.