To improve the rate of construction of neural network based model of power grids fault diagnosis, a method based on multi-output decay radial basis function (MDRBF) neural network for fault diagnosis is proposed. DBRF neural network can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The single-output DRBF (SDRBF) neural network is introduced, and its shortage in fault diagnosis of power grids is analyzed. Since single-output DRBF (SDRBF) neural network can only solve the single-variable output problem, therefore, it can not be used directly in fault diagnosis of power grids. On this basis, a strategy for expanding the SDRBF neural network to the MDRBF neural network is proposed according to the fault characteristic of electric components. MDRBF neural network is able to satisfy the multi-variable output need of fault diagnosis of power grids. A four-bus transmission grid is adopted as a simulation system and the results show that the proposed diagnostic method based on MDRBF neural network is simple and has good fault-tolerance and strong robustness.