Computations of unsteady flows due to inlet distortion driven blade vibrations, characterized by long circumferential wavelengths, typically need to be carried out in multi-passage/whole-annulus domains. In the present work, a single-passage three-dimensional unsteady Navier-Stokes approach has been developed and applied to unsteady flows around vibrating blades of a transonic fan rotor (NASA Rotor-67) with inlet distortions. The phase-shifted periodic condition is applied using a Fourier series based method, “shape-correction,” which enables a single-passage solution to unsteady flows under influences of multiple disturbances with arbitrary interblade phase angles. The computational study of the transonic fan illustrates that unsteady flow response to an inlet distortion varies greatly depending on its circumferential wavelength. The response to a long wavelength (whole-annulus) distortion is strongly nonlinear with a significant departure of its time-averaged flow from the steady state, while that at a short wavelength (two passages) behaves largely in a linear manner. Nevertheless, unsteady pressures due to blade vibration, though noticeably different under different inlet distortions, show a linear behavior. Thus, the nonlinearity of the flow response to inlet distortion appears to influence the aerodynamic damping predominantly by means of changing the time-averaged flow. Good agreements between single-passage solutions and multi-passage solutions are obtained for all the conditions considered, which clearly demonstrates the validity of the phase-shifted periodicity at a transonic nonlinear distorted flow condition. For the present cases, typical CPU time saving by a factor of 5–10 is achieved by the single-passage solutions.