Using high temporal and high spatial resolution observations taken by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory, we present the detailed observational analysis of a high quality quasi-periodic fastpropagating (QFP) magnetosonic wave that was associated with the eruption of a magnetic flux rope and a GOES C5.0 flare. For the first time, we find that the QFP wave lasted during the entire flare lifetime rather than only the rising phase of the accompanying flare as reported in previous studies. In addition, the propagation of the different parts of the wave train showed different kinematics and morphologies. For the southern (northern) part, the speed, duration, intensity variation are about 875 ± 29 (1485 ± 233) km s −1 , 45 (60) minutes, and 4% (2%), and the pronounced periods of them are 106 ± 12 and 160 ± 18 (75 ± 10 and 120 ± 16) seconds, respectively. It is interesting that the northern part of the wave train showed obvious refraction effect when they pass through a region of strong magnetic field. Periodicity analysis result indicates that all the periods of the QFP wave can be found in the period spectrum of the accompanying flare, suggesting their common physical origin. We propose that the quasi-periodic nonlinear magnetohydrodynamics process in the magnetic reconnection that produces the accompanying flare should be important for exciting of QFP wave, and the different magnetic distribution along different paths can account for the different speeds and morphology evolution of the wave fronts.