This paper presents an extended complex Kalman filter artificial neural network for bad-data detection in a power system. The proposed method not only can improve one-by-one detection using the traditional approach as well as enhance its performances. It uses complex-type state variables as the link weighting to largely reduce nodes number and converging speed. In other words, it not only can largely reduce the number of neurons, but also can search out the suitable and available trained variables which do not heuristically need to adjust the link weighting in the learning stage by itself. A 6-bus and IEEE standard of 30-bus power systems are used to verify the feasibility of the proposed method. The results show the convergent behavior of bad-data detection using the proposed method is better than the conventional method.