To solve the problems of large sample size and low optimization efficiency of static approximation model, the least squares support vector regression (LSSVR) based adaptive approximation model with particle swarm optimization (PSO) algorithm was introduced to construct the optimization algorithm. The global and local adaptive approximation models were constructed to reduce the possibility of the optimization algorithm falling into the local optimal solution and to accelerate the convergence process. The Branin function was used as test function to prove the effectiveness of the proposed adaptive PSO-LSSVR approximation model for single-objective optimization problems. The adaptive PSO-LSSVR approximation model was applied to the rapid optimization of boat-tail of GTS model. The upper boat-tail angle, the lower boat-tail angle, the side boat-tail angle and the tail plate length were taken as design variables, and the optimal solution could be obtained only with 31 sample data sets.  And the error of aerodynamic drag coefficient predicted by the approximation model is only 0.18%. The aerodynamic drag of GTS model with optimized boat-tail is reduced by 9.38% after optimization, which proves that the adaptive PSO-LSSVR approximation model optimization method is feasible for fast optimization problem with small samples.