A novel simple cut-cell method for hierarchical Cartesian grid is proposed. Small or split cells which often appear in the cut-cell method are eliminated by a simple projection strategy. In order to evaluate the capability of this method, two-dimensional flow is solved, and the results are compared with the immersed boundary method (IBM) on Cartesian grids. The computational results of inviscid and viscous laminar flow simulations show that the new cut-cell method is superior to IBM in terms of grid convergence of drag force and separation points. The method is extended to turbulent flow simulations using Spalart-Allmaras wall function. The cut-cell method predicts the skin friction accurately, compared to the IBM.