An effective rotational viscosity of vertical alignment (homeotropic) nematic liquid crystal (NLC) cells with negative dielectric anisotropy is derived from a theory of NLCs in which flow effects under the free-slip boundary condition are taken into account. The effective rotational viscosity is a function of the Leslie viscosity coefficients and is much smaller than the rotational viscosity at the initial stage of the director reorientation induced by external electric field to the NLC cells. This is the origin of fast response of vertical alignment of NLC cells.