Consider the following convection di.usion equation,{∂u/∂t+ b1(x; y) ∂u/∂x+ b2(y) ∂u/∂y-(a1∂2u/∂x2 + a2∂2u/∂y2) = f in Ω×J, u(x; y; t) = φ(x; t) onΩ×J,u(x; y; 0) = u0(x; y) inΩ(1)} whereΩ= (0, 1) × (0, 1), J = (0, T), b1(x; y), b2(y) are smooth functions and a1; a2 are positive constants. When convection dominates di.usion, i.e. 0 < a1; a2 << |b|, the general finite di.erence or finite element methods often result numerical oscillation[1]. The upwind method is an e¡Àcient method but is only first order accurate. For one dimensional stable problem with constant coe¡Àcient, [3] presented a high order upwind scheme, but it is di¡Àcult to extend the method to variable coe¡Àcient problem and two dimensional problem. In this paper we give an alternative direction iterative method combining with one dimensional second order upwind scheme for two dimensional problem. It can be as a high speed algorithm on parallel computer. The maximum principle and the second order uniform norm error estimate are obtained. Finally we give some numerical examples.