We have decomposed the 11-cm radio continuum emission of the W51 complex into thermal and non-thermal components. The distribution of the thermal emission has been determined by analyzing HI, CO, and IRAS $60-{mu}m$ data. We have found a good correlation between the 11-cm thermal continuum and the 60- 11m emissions, which is used to obtain the thermal and non-thermal 11-cm continuum maps of the W51 complex. Most of the thermal continuum is emanating from the compact H II regions and their low-density ionized envelopes in W51A and W51B. All the H II regions, except G49.1-0.4 in W51B, have associated molecular clumps. The thermal radio continuum fluxes of the compact H II regions are proportional to the CO fluxes of molecular clumps. This is consistent with the previous results that the total mass of stars in an H II region is proportional to the mass of the associated molecular clump. According to our result, there are three non-thermal continuum sources in W51: G49.4-0.4 in W51A, a weak source close to G49.2-0.3 in W51B, and the shell source W51C. The non-thermal flux of G49.5-0.4 at 11-cm is $~28 Jy$, which is $~25\%$ of its total 11-cm flux. The radio continuum spectrum between 0.15 and 300 GHz also suggests an excess emission over thermal free-free emission. We show that the excess emission can be described as a non-thermal emission with a spectral index ${alpha}{simeq}-1.0 (S_v{propto}V^a)$ attenuated by thermal free-free absorptions at low-frequencies. The non-thermal source close to G49.2-0.3 is weak $(~9 Jy)$. The nature of the source is not known and the reality of the non-thermal emission needs to be confirmed. The non~thermal shell source W51C has a 11-cm flux of $~130Jy$ and a spectral index ${alpha}{simeq}-0.26$.