Employing Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA) multi-wavelength images, we have presented coronal condensations caused by magnetic reconnection between a system of open and closed solar coronal loops. In this Letter, we report the quasi-periodic fast magnetoacoustic waves propagating away from the reconnection region upward across the higher-lying open loops during the reconnection process. On 2012 January 19, reconnection between the higher-lying open loops and lower-lying closed loops took place, and two sets of newly reconnected loops formed. Thereafter, cooling and condensations of coronal plasma occurred in the magnetic dip region of higher-lying open loops. During the reconnection process, disturbances originating from the reconnection region propagate upward across the magnetic dip region of higher-lying loops with the mean speed and mean speed amplitude of 200 and 30 km s$^{-1}$, respectively. The mean speed of the propagating disturbances decreases from $sim$230 km s$^{-1}$ to $sim$150 km s$^{-1}$ during the coronal condensation process, and then increases to $sim$220 km s$^{-1}$. This temporal evolution of the mean speed anti-correlates with the light curves of the AIA 131 and 304 AA~channels that show the cooling and condensation process of coronal plasma. Furthermore, the propagating disturbances appear quasi-periodically with a peak period of 4 minutes. Our results suggest that the disturbances represent the quasi-periodic fast propagating magnetoacoustic (QFPM) waves originating from the magnetic reconnection between coronal loops.
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