An upstream finite difference method suitable for the numerical simulation of high Reynolds number flows of incompressible fluid is considered. An upstream formulation should result in an appropriate central finite difference method when the additional term is turned off. The additional numerical viscosity should essentially be dissipative even if it is applied to the higher-order finite difference scheme. In order to meet these requirements, two types of upstream methods are developed. They are based on the interpolation method of the convective term on the staggered grid system proposed in the accompanying paper. One is the modification of the upstream-biased finite difference (UBD) method. Another is the upstream-shifted interpolation (USI) of the convective term. The proposed schemes are compared with conventional methods using numerical examples for a one-dimensional convection problem with constant velocity. The USI method shows the best features among them and reproduces a reasonable result for the square cavity flow at Reynolds number 10000.