Abstract: In order to solve the shortcomings of the spindle thermal error prediction model established by back propagation (BP) neural network, such as low accuracy, slow convergence speed and easy to fall into the local optimal solution, the K-means++ algorithm and correlation analysis were used to optimize the temperature measurement points and extract the thermal sensitive points, and the genetic algorithm (GA) was used to cross-variation the ant colony. GA-ACO network was constructed to determine the optimal number of hidden layer nodes, weights and thresholds, so as to realize the optimization of BP neural network topology. The thermal error prediction models of spindle based on BP and GA-ACO-BP networks were established, and the thermal error of spindle was measured by five-point method with the five-axis machining center of double turntable as the research object. The thermal error experiment results show that the K-means ++ algorithm combined with Person, Sperman and Kendall correlation analysis can effectively reduce the multicollinearity between temperature variables. Ga-aco-bp model can predict the thermal error of spindle with higher accuracy.