The numerical vertical diffusivity Knum, embeeded in a numerical ocean general circulation model with nonuniform vertical grid, is estimated. It is shown that in a downwelling region, Knum is negative for a grid with grid size increasing with depth. When the grid size increment, or the downward vertical velocity, is large, Knum may exceed the vertical diffusivity specified and may result in a negative effective vertical diffusivity. Therefore care needs to be taken to specify the vertical diffusivity in a numerical model with nonuniform grid, and a lower bound is generally imposed in order to avoid an unphysical negative value. Some possible effects of the negative effective diffusivity are discussed.