The design of radial inflow turbine volute is directly related to the overall performance of the turbine, but due to the asymmetry of its three-dimensional structure, the design method of the volute is still backward relatively to that of turbine rotor. To make the downstream flow of the volute more uniform, the existing one-dimensional and two-dimensional volute design methods generally assume that the mass flow at the volute outlet is uniformly distributed in the circumferential direction. But this hypothesis ignores the existence of the tongue, and inevitably leads to a significantly nonuniform mass flow distribution at the outlet, which imposes a strong excitation to downstream rotor, and can potentially cause high cycle fatigue (HCF) of the rotor. This paper proposes a way to consider the influence of the volute tongue in volute design. A newly published two-dimensional design method is expanded to allow non-uniform circumferential boundary conditions at volute discharge: the mass flow distribution at the discharge is adjusted before and after the volute tongue to reduce the negative influence of the tongue. Three different volutes were designed by this new technique. An experimentally validated numerical method was then used to verify the turbine performance, and it is found that the volutes designed with the non-uniform circumferential boundary conditions indeed reduce the fluctuation of the flow parameters at the volute exit as well as the excitation force on the rotor blades.