Artificial neural network (ANN) provides superior accuracy for nonlinear alternating current (AC) state estimation (SE) in smart grid over traditional methods. However, research has discovered that ANN could be easily fooled by adversarial examples. In this paper, we initiate a new study of adversarial false data injection (FDI) attack against AC SE with ANN: by injecting a deliberate attack vector into measurements, the attacker can degrade the accuracy of ANN SE while remaining undetected. We propose a population-based algorithm and a gradient-based algorithm to generate attack vectors. The performance of these algorithms is evaluated through simulations on IEEE 9-bus, 14-bus and 30-bus systems under various attack scenarios. Simulation results show that DE is more effective than SLSQP on all simulation cases. The attack examples generated by DE algorithm successfully degrade the ANN SE accuracy with high probability.