Aiming at the problem of low measurement accuracy due to the existence of random error in microelectromechanical system (MEMS) gyroscope, a compensation method based on chaotic particle swarm algorithm (CPSO) optimized back propagation (BP) neural network is proposed to deal with the random error. Firstly, The MEMS gyroscope data are collected, the reconstruction parameters are determined and the phase space is reconstructed using the C-C method, and the chaotic properties are analyzed and verified based on the Lyapunov exponent. Then, the reconstructed data are used as the training samples for the BP neural network model. The BP neural network model is trained, and the weights and thresholds of BP neural network are optimized by using the CPSO algorithm, then the optimized model for error compensation is obtained. Finally, ADXRS624 is used to validate the compensation effect of the optimized model in static experiment, and the compensation results are compared with BP model and particle swarm optimization (PSO) model. Experimental analysis results show that the mean and standard deviation of the gyroscope output errors are -5.76×10-4（°）/s and 5.19×10-4（°）/s, which are decreased by 68.6% and 98.4% compared with the BP model, and 52.1% and 93.5% compared with the particle swarm optimization model, respectively. By comparing the error coefficients after compensation for each method using Allan variance identification, the quantization noise, angle random walk and zero bias instability after being compensated by CPSO-BP method are reduced to 0.000 59 μrad, 0.001 51 （(°)·h-1/2） and 2.82 （(°)·h-1）, respectively. The new method has obvious effect in suppressing the random error and can improve the measurement accuracy of MEMS gyroscope.