The hypersonic vehicle has a large number of configuration parameters, and its aerodynamic shape design is very complicated. To overcome this difficulty, a lifting body shape parametric design method is proposed. This method is based on class function/shape function transformation (CST) and power function expression, whose design variables are limited to six ones, which makes it very convenient for configuration analysis and design. By means of orthogonal experiment analysis, the influence of the configuration parameters on volume efficiency and lift-drag ratio of the lifting body was studied, and the ones with the great influence were obtained. Meanwhile, the experiment results found that the configuration parameters have conflict influence on the volume efficiency and lift-drag ratio. Thus, to search for the best configuration parameters, a Kriging surrogate model based multi-objective genetic algorithm was applied to design the lifting body shape, in which the volume efficiency and lift-drag ratio were taken as the two conflict objectives under the constraints of the longitudinal stability and vehicle volume. Numerical results show the efficiency of the method and a uniform Pareto front was obtained. The volume efficiency and lift-drag ratio of the typical optimized shape can be increased by 17.31% and 11.94%, respectively, in comparison with the baseline. Differences of the results gained from the Kriging surrogate model and real physical model are less than 4%. Furthermore, the influences of leading edge blunting on aerodynamic character were researched. The results indicate that, the lift-drag ratio of the lifting body decreases significantly with the increase of blunting radius. It is also found that the optimized results can be extrapolated to the leading edge blunting shapes when aerodynamic character is the unique concern.