In this paper, an unstructured, collocated finite volume method for solving the Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives were determined by the Gauss theorem. The proposed method could provide control volumes with arbitrary geometry and preserve the second-order accuracy even if highly distorted grids are used. Although arbitrary number of cell faces can be used, the hybrid quadrilateral/triangular grids are more desirable for the simplicity of implementation and applications to engineering problems. The pressure-velocity coupling was treated using a SIMPLE-like algorithm. The Generalized Minimum Residual (GMRES) method with the Incomplete LU (ILU) preconditioner was used to solve linear equations. Four test cases were studied for validating the proposed method. In using this method, grid quality is not important. Thus, engineers can pay mostly attention to physical mechanism of problems. Turbulence models can be simply integrated and the method can be straightforwardly extended to treat three-dimensional problems.