We propose a novel adversarial speaker adaptation (ASA) scheme, in which adversarial learning is applied to regularize the distribution of deep hidden features in a speaker-dependent (SD) deep neural network (DNN) acoustic model to be close to that of a fixed speaker-independent (SI) DNN acoustic model during adaptation. An additional discriminator network is introduced to distinguish the deep features generated by the SD model from those produced by the SI model. In ASA, with a fixed SI model as the reference, an SD model is jointly optimized with the discriminator network to minimize the senone classification loss, and simultaneously to mini-maximize the SI/SD discrimination loss on the adaptation data. With ASA, a senone-discriminative deep feature is learned in the SD model with a similar distribution to that of the SI model. With such a regularized and adapted deep feature, the SD model can perform improved automatic speech recognition on the target speaker's speech. Evaluated on the Microsoft short message dictation dataset, ASA achieves 14.4% and 7.9% relative word error rate improvements for supervised and unsupervised adaptation, respectively, over an SI model trained from 2600 hours data, with 200 adaptation utterances per speaker.