In robust design optimization (RDO) of electrical machines, the cases with random uncertainty and interval uncertainty are generally investigated separately. The uncertainty quantification is based on the random method and interval method, respectively. For problems with hybrid uncertainties, the uncertainty analysis methods for a single type of uncertainties may no longer be applicable as both the random and interval methods are required for the uncertainty qualification. This poses considerable challenges to the hybrid uncertainty modeling, numerical calculation, and design optimization. This paper proposes an efficient robust optimizer based on the evolutionary algorithms and the polynomial chaos Chebyshev interval (PCCI) method for RDO of electrical machines with hybrid uncertainties. With the potential candidate filtering in the population of each iteration and effective robustness assessment by the PCCI method, the optimization can be conducted efficiently. A design example of a brushless DC motor considering hybrid uncertainties is analyzed and optimized. The results confirm the feasibility of the proposed method.