Many systems in the real world can be described by evolving models of complex network, one of which is power system. Classical network models show great inconsistence with practical power grids. Based on the essential evolution characteristics of power grid, we propose a new local-world evolving network model for complex power grid, which exists in many physical complex networks. The statistical properties and dynamics of the proposed model are analytically studied. It is found that the degree distribution of this new model has a power-law tail, and its scaling exponent is between 3 and ∞. Numerical simulations for West American power grid and North China power grid and their comparison with random network and scale-free network indicate that the new evolving network model captures the essential features of real-world power grid. Furthermore, it is proved that power grid is neither a random network nor a scale-free network.