A high order compact finite difference scheme is proposed to solve the three-dimensional unsteady convection diffusion equation with variable convection coefficients.The scheme is of fourth order in space and second order in time.A multigrid algorithm is presented to overcome the difficulties when traditional relaxation methods are used to treat the implicit difference schemes at each time step and a fast solution is obtained.Numerical experiments are employed to show that the present method is stable and yields accurate solutions for high Reynolds number problems.