We investigate the use of generative adversarial networks (GANs) in speech dereverberation for robust speech recognition. GANs have been recently studied for speech enhancement to remove additive noises, but there still lacks of a work to examine their ability in speech dereverberation and the advantages of using GANs have not been fully established. In this paper, we provide deep investigations in the use of GAN-based dereverberation front-end in ASR. First, we study the effectiveness of different dereverberation networks (the generator in GAN) and find that LSTM leads a significant improvement as compared with feed-forward DNN and CNN in our dataset. Second, further adding residual connections in the deep LSTMs can boost the performance as well. Finally, we find that, for the success of GAN, it is important to update the generator and the discriminator using the same mini-batch data during training. Moreover, using reverberant spectrogram as a condition to discriminator, as suggested in previous studies, may degrade the performance. In summary, our GAN-based dereverberation front-end achieves 14%-19% relative CER reduction as compared to the baseline DNN dereverberation network when tested on a strong multi-condition training acoustic model.