We report non-perturbative time-dependent quantal studies on the superexchange mechanism in electron transfer processes. In our one-dimensional model, the donor and acceptor states are coupled through an intermediate bridge state that may have higher energy than both the donor and acceptor states. The electron transfer dynamics are simulated by numerically solving the exact time-dependent Schrodinger equation. Electron transfer rates are extracted from the population decay of the donor state or the buildup of the acceptor. This approach is very efficient and applicable in cases where perturbative methods fail. It also gains insight into dynamical evolution of electron transfer systems.