The self-propulsion of a 3-D flapping flexible plate in a stationary fluid is numerically studied by an immersed boundary- lattice Boltzmann method for the fluid flow and a finite element method for the plate motion. When the leading-edge of the plate is forced to heave sinusoidally, the entire plate starts to move freely as a result of the fluid-structure interaction. Based on our simula- tion and analysis on the dynamical behaviors of the flapping flexible plate, we have found that the effect of plate aspect ratio on its propulsive properties can be divided into three typical regimes which are related to the plate flexibility, i.e. stiff, medium flexible, and more flexible regime. It is also identified that a suitable structure flexibility, corresponding to the medium flexible regime, can improve the propulsive speed and efficiency. The wake behind the flapping plate is investigated for several aspect ratios to demon- strate some typical vortical structures. The results obtained in this study can provide some physical insights into the understanding of the propulsive mechanisms in the flapping-based locomotion.