A neural network-based decoder, based on a long short-term memory (LSTM) network, is proposed to solve the problem of high decoding delay caused by the poor parallelism of existing decoding algorithms for turbo codes. The powerful parallel computing and feature learning ability of neural networks can reduce the decoding delay of turbo codes and bit error rates simultaneously. 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. 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. Furthermore, the results demonstrate that the proposed decoder can be used in communication systems with various turbo codes and that it solves the problem of high delay in serial iterative decoding.