A small-world neural network has stronger generalization ability with high transfer efficiency than that of the regular neural networks. This paper presents two novel small-world neural networks

the Watts-Strogatz small-world based on a BP neural network (WSBP) and a Newman-Watts small-world neural network based on a BP neural network (NWBP)

related to previous research of complex networks. The algorithms are developed separately by adopting WS and NW small-world networks as their topological structures

and their derivation and convergence criterion are progressively discussed. After that

the proposed models are subsequently tested by two typical nonlinear functions which confirm their significant improvement over the regular BP networks and other algorithms. Finally

a wind power prediction system is advanced to verify their generalization abilities

and show that the models are practically feasible and effective with improved accuracy and acceptable forecasting errors caused by wind fluctuation and randomness with a time scale up to 24 h.