Large-scale extreme-ultraviolet waves commonly exhibit as single wave front and are believed to be caused by coronal mass ejections. Utilizing high spatiotemporal resolution imaging observations from the Solar Dynamics Observatory, we present two sequentially generated wave trains originating from the same active region: a narrow quasiperiodic fast-propagating (QFP) wave train that propagates along the coronal loop system above the jet and a broad QFP wave train that travels along the solar surface beneath the jet. The measurements indicate that the narrow QFP wave train and the accompanying flare’s quasiperiodic pulsations (QPPs) have nearly identical onsets and periods. This result suggests that the accompanying flare process excites the observed narrow QFP wave train. However, the broad QFP wave train starts approximately 2 minutes before the QPPs of the flare, but it is consistent with the interaction between the unwinding jet and the solar surface. Moreover, we find that the period of the broad QFP wave train, approximately 130 s, closely matches that of the unwinding jet. This period is significantly longer than the 30 s period of the accompanying flare’s QPPs. Based on these findings, we propose that the intermittent energy release of the accompanying flare excited the narrow QFP wave train confined propagating in the coronal loop system. The unwinding jet, rather than the intermittent energy release in the accompanying flare, triggered the broad QFP wave train propagating along the solar surface.