A new numerical method is presented in this paper to simulate rotor/stator interaction in turbomachinery by use of a vortex method based on a Lagrangian frame. The algorithm takes the result from steady solution as input, which can give an initial description of the unsteady disturbance flow field. To calculate the unsteady response to these disturbances, the Lagrangian vortex method is used to capture the convective process, and the deterministic vortex scheme to approximate the viscous diffusion process. The application of Baldwin-Lomax turbulence model in wakes is developed, so as to overcome the difficulties such as the much higher calculated viscosity in the outer region than that in the boundary regions, and the difficulty in continuously tracing moving wake centerlines encounted by other numerical methods. The agreement between the computational and experimental results is generally good. The sweeping characteristic of wakes, the influence of unsteadiness on incidence and the decaying features of unsteady velocities, pressure are included in the paper.