The tip-clearance flow in a cascade was numerically simulated by solving the RANS equations of incompressible fluids. The computational model was based upon the artificial compressibility formulation proposed by Chorin. The Baldwin-Lomax turbulence model was used to make the governing equations closed. For the specific structure of tip-clearance flow, a multi-block grid structure was adopted to facilitate numerical computations. The comparison of numerical results with experimental data indicates that the present method is capable of simulating tip-clearance flows with satisfactory accuracy.