This paper presents a model for predicting music complexity as perceived by cochlear implant (CI) users. To this end, 10 CI users and 19 normal-hearing (NH) listeners rated 12 selected music pieces on a bipolar music complexity scale and 5 other perception-related scales. The results indicate statistically significant differences in the ratings between CI and NH listeners. In particular, the ratings among different scales were significantly correlated for CI users, which hints at a common, hidden scale. The median complexity ratings by CI listeners and features accounting for high-frequency energy, spectral center of gravity, spectral bandwidth, and roughness were used to train a linear principal component regression model for an average CI user. The model was evaluated by means of cross-validation and using an independent database of processed chamber music signals for which music preferences scores by CI users were available. The predictions indicate a clear linear relationship with the preference scores, confirming the negative correlation between music complexity and music preference for CI users found in previous studies. The proposed model is a first step toward an instrumental evaluation procedure in the emerging field of music processing for CIs.