The authors establish an incomplete information Bertrand duopoly model to forecast the essential influence on the equilibrium profit of stateowned commercial bank and the social welfare from the variety of the expectation by foreign bank, when the stateowned commercial bank has the information advantage about the status of saving market. We find that the equilibrium interest rate of the stateowned commercial bank would set down lower, as the expectation probability for the appearing of high spontaneous deposit rises. The equilibrium profit of stateowned commercial bank and the social welfare will increase when the foreign bank has the optimistic expectation for the status of saving market. The information advantage of stateowned commercial bank could become the competition advantage.