  The middle-aged supernova remnant (SNR) W51C is an interesting source for the
interaction of the shell with a molecular cloud. The shell emits intense radio
synchrotron photons, and high-energy gamma-rays from the remnant have been
detected using the {\it Fermi} Large Area Telescope (LAT), the H.E.S.S.
telescope, and the Milagro gamma-ray observatory. Based on a semi-analytical
approach to the nonlinear shock acceleration process, we investigate the
multiband nonthermal emission from W51C. The result shows that the radio
emission from the remnant can be explained as synchrotron radiation of the
electrons accelerated by a part of the shock flowing into the ambient medium.
On the other hand, the high-energy gamma-rays detected by the {\it Fermi} LAT
are mainly produced via proton-proton collisions of the high-energy protons
with the ambient matter in the molecular cloud overtaken by the other part of
the shock. We propose a possible explanation of the multiband nonthermal
emission from W51C, and it can be concluded that a molecular cloud overtaken by
a shock wave can be an important emitter in GeV $\gamma$-rays.
