In　this　paper,　we　consider　a　singular　perturbation　elliptic-parabolic　partial　differential　equation　for　periodic　boundary　value　problem,　and　construct　a　difference　scheme.　Using　the　method　of　decomposing　the　singular　term　from　its　solution　and　combining　an　asymptotic　expansion　of　the　equation,　we　prove　that　the　scheme　constructed　by　this　paper　converges　uniformly　to　the　solution　of　its　original　problem　with　O(τ　+　h2).