A new theoretical model has been proposed to explain the origin of the double-peak emission observed characteristically in m-plane InGaN quantum wells (QWs). Although the emission spectrum with a double-peak structure is generally regarded as evidence of In compositional phase separation or extended crystal defects that generate localized energy states, such crystal irregularities cannot be observed by transmission electron microscopy or three-dimensional atom probe in the QWs. It has been clarified, by our model, that only the slowly decaying tailing of the density of states can cause the double-peak structure. This is consistent with experimental results, and furthermore, the measured temperature and In composition dependences of photoluminescence spectra with the double-peak emission can also be successfully reproduced by theoretical calculation based on our model.