This paper presents a new damping controller design based on fuzzy wavelet neural network (FWNN) to damp the multi-machine power system low frequency oscillations. The error between the desired system output and the output of control object is directly utilized to tune the network parameters. The orthogonal least square (OLS) algorithm is used to purify the wavelets for each rule and determine the number of fuzzy rules and network dimension. In this paper, Shuffled Frog Leaping Algorithm (SFLA) is proposed for learning of FWNN and to find the optimal values of the parameters of the FWNN damping controller. To illustrate the capability of the proposed approach, some numerical results are presented on a 2-area 4-machine and a 5-area-16-machine power system. To show the effectiveness and robustness of the designed controller, the case studies are tested under two conditions: applying a line-to-ground fault at a bus and applying a three phase fault at a bus. Furthermore, to make a comparison, the proposed approach is compared with a classical based method and a FWNN based genetic algorithm approach, which is adopted from literature, through eigenvalue analysis, time- domain simulation and some performance indices. The simulation results show the superiority and capability of the proposed FWNN damping controller. Manuscript profile