The observational analysis is performed to study the excitation mechanism and the propagation properties of a quasi-periodic fast-propagating ( QFP ) magnetosonic wave . The QFP wave was associated with the eruption of a nearby mini-filament and a small B4 GOES flare , which may indicate that the generation of a QFP wave do not need too much flare energy . The propagation of the QFP wave was along a bundle of funnel-shaped open loops with a speed of about 1100 \pm 78 km s ^ { -1 } , and an acceleration of -2.2 \pm 1.1 km s ^ { -2 } . Periodicity analysis indicates that the periods of the QFP wave are 43 \pm 6 , 79 \pm 18 second . For the first time , we find that the periods of the QFP wave and the accompanying flare are inconsistent , which is different from the findings as reported in previous studies . We propose that the present QFP wave was possibly caused by the mechanism of dispersive evolution of an initially broadband disturbance resulted from the nearby mini-filament eruption .