Using symplectic integrators and staggered spatial differences to establish a new high-order Symplectic Finite-Difference Time-Domain scheme (SFDTD(4,4)) for solving time-dependent Schr?dinger equation. The fourth-order accuracy difference scheme for the second derivative of the space segment is to obtain the time evolution of the multi-dimensional system and then introducing the fourth order symplectic integrator for discrete; the numerical stability is obtained with SFDTD(4,4) scheme, one-or multi-dimensional stability conditions for Schrdinger equation with nonzero potential energy are also derived; the perfect absorbing boundary condition of SFDTD(4,4) scheme for quantum devices is achieved by the concept of stretching coordinate. The simulated results of a one-dimensional quantum well and metal MOSFET confirm the preference of the SFDTD(4,4) scheme over the traditional finite-difference time-domain scheme. The SFDTD(4,4) scheme, which is high-order-accurate and energy conserving, is well suited for long term simulation.The results can be used as a necessary reference for the design of new quantum devices.