This paper proposes the optimal design of stator shape for cogging torque reduction of single-phase brushless DC (BLDC) motor with asymmetric notch. This method applied size and position of asymmetric notches to tapered teeth of stator for single-phase BLDC motor. Which affects the variation of the residual flux density of the permanent magnet. The process of optimal design included the extraction of the sampling point by using Latin Hypercube Sampling(LHS), and involved the creation of an approximation model by using kriging method. Also, the optimum point of the design variables were discovered by using the Genetic Algorithm(GA). Finite element analysis was used to calculate the characteristics analysis and cogging torque. As a result of finite element analysis, cogging torque were reduced approximately 39.2% lower than initial model. Also experimental result were approximately 38.5% lower than initial model. The period and magnitude of the cogging torque were similar to the results of FEA.