As a high-precision instrument, electronic pressure scanners have a crucial role in multi-point pressure measurements. However, the internal piezoresistive components drift with temperature, and this phenomenon has become a key factor restricting the accuracy. In this study, a hybrid algorithm based on back propagation neural network (BPNN) with particle swarm optimization (PSO) and gravity search algorithm (GSA) is reported for multi-channel temperature compensation to solve this problem Fundamentally, the global optimization search capability of GSA and the fast local convergence advantage of PSO are utilized so that the model parameters of the BPNN are guaranteed to be reliable and the efficiency of its execution is further improved. To this end, the temperature data between −40 °C and 70 °C obtained through the calibration experimental system are analyzed for compensation of the electronic pressure scanner from the 0 to 700 kPa adiabatic range. The results show that, compared with BP neural network, radial basis function (RBF) neural network, and PSO-BP method, the new PSOGSA-BP approach has higher accuracy in pressure sensor temperature compensation, in which the absolute error is only 0.2301 kPa and the full-scale error is 0.03% full scale. In addition, the method can be applied to electronic pressure scanners with stronger generalization and demonstrated to be suitable for temperature compensation.