In recent years, large pre-trained language models (PLMs) have achieved remarkable performance on many natural language processing benchmarks. Despite their success, prior studies have shown that PLMs are vulnerable to attacks from adversarial examples. In this work, we focus on the named entity recognition task and study context-aware adversarial attack methods to examine the model's robustness. Specifically, we propose perturbing the most informative words for recognizing entities to create adversarial examples and investigate different candidate replacement methods to generate natural and plausible adversarial examples. Experiments and analyses show that our methods are more effective in deceiving the model into making wrong predictions than strong baselines.