Abstract: The formulation of a control-volume-based on finite-element method (CVFEM) for two-dimensional convection-diffusion equaitons is presented.It has a main advantage in capability of the obtained discretization equation to be solved with point-by-point and conjugate gradient iteration method,so that it is more suitable to complex geometrical fields and can save much more computer memory.Some numerical examples proved that the accuracy to any high Peclet number is quite encouraging.