This paper presents the result of Large Eddy Simulation (LES) of a spatially developing plane turbulent jet flow. Because simulation of the flow is sensitive to numerical disturbance due to inadequate treatment of outflow velocity boundary condition just as the flow is easily influenced by external disturbance in experiments, it prevented from the success for simulating the flow. Here a new outflow velocity boundary condition of LES is proposed based on physical insight of the spatially developing plane turbulent jet flow. The result of LES using this outflow boundary condition exhibits that many essential features of the unsteady spatially developing plane turbulent jet flow are reproduced by the present computation.