The output of a MEMS gyroscope is easily influenced by temperature, which has led to a bottleneck in the development of gyroscopes. Therefore, to eliminate the temperature error of gyroscopes, a parallel processing algorithm based on variational modal decomposition optimized by genetic particle swarm optimization variational modal decomposition (GPSO-VMD) and an improved backpropagation (BP) neural network is proposed in this paper. First, for the original output signal of a gyroscope, GPSO is adopted to search for the optimal parameters for VMD. Next, the optimal parameters (kbest, αbest) are applied to VMD to obtain intrinsic mode functions (IMFs). Then, according to the calculated result of multiscale permutation entropy (MPE), IMFs are divided into three categories: noise items, mixed items, and drift items. The three categories are treated separately: noise items are removed directly, mixed items are filtered, and for drift items, temperature errors are eliminated by using an improved BP neural network. The final signal is then obtained through reconstruction. Compared with the traditional optimization algorithm, GPSO has excellent global search ability and strong convergence. The BP neural network improved by the genetic algorithm (GA) overcomes the problem of easily falling into a local optimum, and excellent prediction performance is achieved. Experimental results demonstrate the feasibility of this proposed hybrid model in eliminating gyroscope temperature errors.