Aiming at the problem that Backtracking Search optimization Algorithm （BSA） is easy to premature and has weak local development ability in the optimization of kernel function parameters and regularization parameters of Least Square Support Vector Machine （LSSVM）， an integrated prediction model named CABSA-LSSVM was proposed. Firstly， the Cauchy population generation strategy was used to improve the diversity of historical populations， so that the algorithm was not easy to fall into the local optimal solution. Then， the adaptive mutation factor strategy was used to balance the global exploration and local development abilities of the algorithm by adjusting the mutation scale coefficient. Finally， the improved Cauchy Adaptive Backtracking Search Algorithm （CABSA） was used to optimize the LSSVM to form a new integrated prediction model. Ten UCI datasets were selected for numerical experiments. The results show that the proposed model CABSA-LSSVM has the best regression prediction performance when the population size is 80. Compared with the LSSVMs optimized by the standard BSA， Particle Swarm Optimization （PSO） algorithm， Artificial Bee Colony （ABC） algorithm and Grey Wolf Optimization （GWO） algorithm， the proposed model has the coefficient of determination increased by 1.21%-15.28%， the prediction error reduced by 6.36%-29.00%， and the running time reduced by 5.88%-94.16%. In conclusion， the proposed model has high prediction accuracy and fast computation speed.