This paper examines the dynamics and conditions for stabilization when the central bank adopts a monetary policy with discretion in the growth rate of a nominal money supply, especially during a ‘short run’ Keynesian model with a liquidity trap.　In addition, the formalization of the expected inflation is a mixture of ‘forward looking’ and ‘backward looking’.　The framework of the macro model is based on Asada （［7］）. We focus on the mixed-type formalization of expected inflation with ‘backward looking’ to evaluate the performance of the policy.　If the speed of the aggregate demand influenced by the growth rate of real money is sufficiently small positive value, even though credibility of inflation targeting is not sufficient, the central bank can stabilize and optimize a macro economy with a discretionary commitment policy.　However, if the speed of adjustment of the aggregate demand influenced by the growth rate of the real money is larger than 1, the discretionary commitment policy does not accomplish stabilization and optimization in the system. JEL Classification:E52, E61, E62