We observed the resonant sidebands similar to the Kelly sidebands, but caused by the coupling between continuous-wave (CW) and dispersive waves (DWs) in a mode-locked ring fiber laser for the first time, to the best of our knowledge. The coupling between the CW and DWs is a linear process, which is different from the previously observed parametric sub-sidebands. The regimes of the CW-induced sidebands are discussed. The experimental results agree both qualitatively and quantitatively with theoretical analysis. The results enrich the nonlinear dynamics of ultrafast fiber lasers and may have potential in optically controlling mode-locked lasers.