While right‐censored data are very common in survival analysis, they may also occur in the case of count data. The literature contains models to treat such right‐censored count data. In this paper, we want to address issues of heterogeneity and clustering in this context. We propose a finite mixture of censored Poisson regressions to accommodate heterogeneity and also identify clusters in right‐censored count data. We also develop an expectation maximization algorithm to facilitate the estimation of such models and discuss the computational aspects of the proposed algorithm. We then present results based on simulated data to show the effect of censoring in estimation. We also present a marketing application of the proposed approach involving the number of renewals of magazine subscriptions.