The possibility and conditions of stochastic acceleration of an electron in plasma by a standing wave is discussed and numerically calculated. The analytical results show that the stochasticity of the motion of the electron is due to overlap of the two resonances imbedded in the interaction between the electron and the standing wave. The threshold of stochastic acceleration is evaluated analytically and numerically. The energy of stochastic acceleration of the electron is also calculated numerically with the trajectories of the electron being traced by using Poincare's surface-of-sectiun plot technique.