A director model on the dynamics of a lipid or bio- membrane is constructed. In this model, we derive the evolving equations of the surface geometric quantities and the dynamic equations of the membrane, taking into account the effects of elasticity, viscosity, and membrane incompressibility, with and without the presence of bulk fluid. We also consider the effect of local spontaneous curvature which may arise from the presence of membrane proteins. Numerical simulations on the cylindrical and axial-symmetrical membrane and linearization analysis on the planar membrane are carried out based on the director model and its reduced model. The results of the linearization analysis appear to be consistent with the experiments for low wavenumber case and with the MD simulation for the high wavenumber case.