Neoclassical ion viscosity of a steady tokamak plasma with large mass flow is calculated in a general geometry. In addition to the usual ‘‘resonant’’ contribution, the ‘‘nonresonant’’ contribution has been evaluated. It is found that the nonresonant contribution is not small compared to the resonant contribution when the poloidal rotation speed is large. The viscosity evaluation has been reduced to one‐dimensional integrals. Furthermore, simple analytic formula for the viscosity coefficients are suggested. The velocity strain, which is the source of the viscosity, is also analyzed in detail.