In order to reduce the thermal error caused by spindle running,a hybrid algorithm is established to optimize the Back Propagation(BP) neural network prediction model,and the accuracy of prediction is verified by experiments. The shortcomings of simulated annealing algorithm and particle swarm optimization(PSO) algorithm were analyzed,and the simulated annealing algorithm coupled PSO algorithm was used to give the optimization steps of the hybrid algorithm. Using BP neural network structure, a thermal error prediction model of machine tool spindle was constructed,and a hybrid algorithm is used to optimize the BP neural network prediction model. The accuracy of thermal error prediction of spindle was verified by experiments and compared with that before optimization. The results show that the maximum error value of the Y axis direction is reduced from 73 μm to 23 μm by the BP neural network prediction model optimized by the hybrid algorithm,and the maximum error value produced in the direction of the Z axis is reduced from 75 μm to 26 μm.At the same time, the overall error of machine tool spindle has a smaller fluctuation range.The hybrid algorithm is used to optimize the BP neural network prediction model,which is used for online thermal error compensation of machine tools spindle and the machining accuracy is improved.