Long Short-Term Memory (LSTM) is the primary recurrent neural networks architecture for acoustic modeling in automatic speech recognition systems. Residual learning is an efficient method to help neural networks converge easier and faster. In this paper, we propose several types of residual LSTM methods for our acoustic modeling. Our experiments indicate that, compared with classic LSTM, our architecture shows more than 8% relative reduction in Phone Error Rate (PER) on TIMIT tasks. At the same time, our residual fast LSTM approach shows 4% relative reduction in PER on the same task. Besides, we find that all this architecture could have good results on THCHS-30, Librispeech and Switchboard corpora.