With the deployment of new elements in the smart grid, traditional state estimation methods are challenged by growing dynamics and system size. Artificial neural network (ANN) based AC state estimation has been shown to provide faster results than traditional methods. However, researchers have discovered that ANNs could be easily fooled by adversarial examples. In this paper, we initiate a new study of adversarial false data injection attacks against ANN-based state estimation. By injecting a deliberate attack vector into measurements, the attacker can degrade the accuracy of ANN state estimation while remaining undetected. We propose two algorithms to generate the attack vectors, a population-based algorithm (differential evolution or DE) and a gradient-based algorithm (sequential least square quadratic programming or SLSQP). 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 the DE algorithm successfully degrade the ANN state estimation accuracy with high probability (more than 80% in all simulation cases), despite having a small number of compromised meters and low injection strength. We further discuss the potential defense strategy to mitigate such attacks, which provides insights for robustness improvement in future research. (c) 2021 Elsevier Ltd. All rights reserved.