Centrifugal compressors are widely used in ships, automobiles, aerospace and other fields. At present, the centrifugal compressor is usually designed with splitter blades to achieve a high pressure ratio and avoid airflow blockage at the leading edge throat of the main blade. This paper offers a multivariable optimization method for splitter blades design of centrifugal compressor. The length and circumferential position of the splitter blades are coupled to optimize the isentropic efficiency by using the Latin hypercube sampling, Regression Kriging algorithm and genetic algorithm. After optimization, the results show that the length of the splitter blades is shorter and its position is inclined to the pressure surface of the main blades. The maximum isentropic efficiency increased by 0.62%, the flow rate of the impeller surge point increased by 1.78%, and the flow rate of the plug point increased by 1.74%. After optimization, the low-speed zone of the flow field in the impeller decreases and the internal passages become more smooth. Besides, the degree of airflow obstruction is reduced, and the overall efficiency of the impeller is improved. The multivariable optimization method which is based on the Regression Kriging algorithm has certain universality and can provide important reference for the splitter blades design of centrifugal compressors and other turbomachinery.