A neural network-based decoder, based on a long short-term memory (LSTM) network, is proposed to solve the problem that large decoding delay and performance degradation under non-Gaussian noise due to poor parallelism of existing turbo decoding algorithms. The proposed decoder refers to a unique component coding concept of turbo codes. First, each component decoder is designed based on an LSTM network. Next, each layer of the component decoder is trained, and the trained weights are loaded into the turbo code decoding neural network as initialization parameters. Then, the turbo code decoding network is trained end-to-end. Finally, a complete turbo decoder is realized. The structural advantage of turbo code component coding is fully considered in the design process, and the problem of decoding delay caused by the existence of interleaver is cleverly avoided. The introduction of deep learning technology provides a new idea to solve the traditional communication problems. Simulation results show that the performance of the proposed decoder is improved by 0.5–1.5 dB compared with the traditional serial decoding algorithm in Gaussian white noise and t-distribution noise. When BER performance is close, the LSTM decoder requires half or even less than that of BCJR. Moreover, the results demonstrate that the proposed decoder is adaptive and can be applied to communication systems with various turbo codes. The LSTM decoder shows lower bit error rate, computational complexity and higher decoding efficiency under the same conditions. Therefore, it is necessary to study the turbo code decoding technology based on deep learning combined with the actual channel environment.