A deep learning approach has been widely applied in sequence modeling problems. In terms of automatic speech recognition (ASR), its performance has significantly been improved by increasing large speech corpus and deeper neural network. Especially, recurrent neural network and deep convolutional neural network have been applied in ASR successfully. Given the arising problem of training speed, we build a novel deep recurrent convolutional network for acoustic modeling and then apply deep residual learning to it. Our experiments show that it has not only faster convergence speed but better recognition accuracy over traditional deep convolutional recurrent network. In the experiments, we compare the convergence speed of our novel deep recurrent convolutional networks and traditional deep convolutional recurrent networks. With faster convergence speed, our novel deep recurrent convolutional networks can reach the comparable performance. We further show that applying deep residual learning can boost the convergence speed of our novel deep recurret convolutional networks. Finally, we evaluate all our experimental networks by phoneme error rate (PER) with our proposed bidirectional statistical n-gram language model. Our evaluation results show that our newly proposed deep recurrent convolutional network applied with deep residual learning can reach the best PER of 17.33\% with the fastest convergence speed on TIMIT database. The outstanding performance of our novel deep recurrent convolutional neural network with deep residual learning indicates that it can be potentially adopted in other sequential problems.