To improve the numerical simulation of incompressible fluid flow using rectangular grids of non-uniform spacings, a fully consistent and conservative finite-difference method is proposed for the convection term of Navier-Stokes equation of motion. When the mass continuity is satisfied numerically, the present schemes have complete conpatibility between the divergence form and the gradient form. In addition, the kinetic energy is conserved numerically according to the condition. These properties are evaluated by the numerical examples for laminar flow in a square cavity.