We apply a recently developed quasi-diabatic (QD) propagation scheme to simulate proton-coupled electron transfer (PCET) reactions. This scheme enables a direct interface between an accurate diabatic dynamics approach and the adiabatic vibronic states of the coupled electron-proton subsystem. It explicitly avoids theoretical efforts to preconstruct diabatic states for the transferring electron and proton or reformulate a diabatic dynamics method to the adiabatic representation, both of which are nontrivial tasks. Using a partial linearized path-integral approach and symmetrical quasi-classical approach as the diabatic dynamics methods, we demonstrate that the QD propagation scheme provides accurate vibronic dynamics of PCET reactions and reliably predicts the correct reaction mechanism without any a priori assumptions. This work demonstrates the possibility to directly simulate challenging PCET reactions by using accurate diabatic dynamics approaches and adiabatic vibronic information.