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In order to improve the performance of a micro-electro-mechanical system (MEMS) accelerometer, three algorithms for compensating its temperature drift are proposed in this paper, including deep long short-term memory recurrent neural network (DLSTM-RNN, short DLSTM), DLSTM based on sparrow search algorithm (SSA), and DLSTM based on improved SSA (ISSA). Moreover, the piecewise linear approximation (PLA) method is employed in this paper as a comparison to evaluate the impact of the proposed algorithm. First, a temperature experiment is performed to obtain the MEMS accelerometer’s temperature drift output (TDO). Then, we propose a real-time compensation model and a linear approximation model for neural network methods compensation and PLA method compensation, respectively. The real-time compensation model is a recursive method based on the TDO at the last moment. The linear approximation model considers the MEMS accelerometer’s temperature and TDO as input and output, respectively. Next, the TDO is analyzed and optimized by the real-time compensation model and the three algorithms mentioned before. Moreover, the TDO is also compensated by the linear approximation model and PLA method as a comparison. The compensation results show that the three neural network methods and the PLA method effectively compensate for the temperature drift of the MEMS accelerometer, and the DLSTM + ISSA method achieves the best compensation effect. After compensation by DLSTM + ISSA, the three Allen variance coefficients of the MEMS accelerometer that bias instability, rate random walk, and rate ramp are improved from 5.43×10−4mg, 4.33×10−5mg/s12, 1.18×10−6mg/s to 2.77×10−5mg, 1.14×10−6mg/s12, 2.63×10−8mg/s, respectively, with an increase of 96.68% on average.