We report the first unambiguous quasi-periodic large-scale extreme-ultraviolet (EUV) wave or shock that was detected by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. During the whip-like unwinding eruption of a small filament on 2012 April 24, multiple consecutive large-scale wavefronts emanating from AR11467 were observed simultaneously along the solar surface and a closed transequatorial loop system. In the meantime, an upward propagating dome-shaped wavefront was also observed, whose initial speed and deceleration are about 1392 km s(-1) and 1.78 km s(-2), respectively. Along the solar surface, the quasi-peridoic wavefronts had a period of about 163 +/- 21 s and propagated at a nearly constant speed of 747 +/- 26 km s(-1); they interacted with active region AR11469 and launched a sympathetic upward propagating secondary EUV wave. The wavefronts along the loop system propagated at a speed of 897 km s(-1), and they were reflected back at the southern end of the loop system at a similar speed. In addition to the propagating waves, a standing kink wave was also present in the loop system simultaneously. Periodicity analysis reveals that the period of the wavefronts was consistent with that of the unwinding helical structures of the erupting filament. Based on these observational facts, we propose that the observed quasi-periodic EUV wavefronts were most likely excited by the periodic unwinding motion of the filament helical structures. In addition, two different seismological methods are applied to derive the magnetic field strength of the loop system, and for the first time the reliability of these inversion techniques are tested with the same magnetic structure.