Recent advances in laser technology have enabled tremendous progress in light-induced molecular reactions, at the heart of which the breaking and formation of chemical bonds are located. Such progress has been greatly facilitated by the development of an accurate quantum-mechanical simulation method, which, however, does not necessarily accompany clear dynamical scenarios and is rather computationally heavy. Here, we develop a wave-packet surface propagation (WASP) approach to describe the molecular bond-breaking dynamics from a hybrid quantum-classical perspective. Via the introduction of quantum elements including state transitions and phase accumulations to the Newtonian propagation of the nuclear wave packet, the WASP approach naturally comes with intuitive physical scenarios and accuracies. It is carefully benchmarked with the H_{2}^{+} molecule and is shown to be capable of precisely reproducing experimental observations. The WASP method is promising for the intuitive visualization of light-induced molecular dynamics and is straightforward extensible towards complex molecules.