This paper proposes a low complexity algorithm for calculating the soft decision metric of forward error correction codes. In order to reduce the complexity of LLR calculation, neural network training can be used to fit the relationship between input and output during exact LLR calculation. The trained network can skip the complex training process and directly estimate the LLR value. We use random signal-to-noise ratio (SNR) and received signals as the input layer of the neural network, and use the precisely calculated soft decision information as the output layer of the network. After training, the network can accurately estimate the LLR of the received symbols. The performance of 16QAM and 64QAM transmission system using the proposed algorithm and the exact LLR calculation algorithm in the AWGN channel with polar code as the encoding algorithm are presented, respectively. The simulation results show that the proposed algorithm has a similar bit error rate performance to traditional exact calculation algorithms, but with much lower complexity. The proposed algorithm can be applied in various decoding situations that require LLR calculation.