This paper proposes a non-parametric Bayesian approach to detect the change-points of intensity rates in the recurrent-event context and cluster subjects by the change-points. Recurrent events are commonly observed in medical and engineering research. The event counts are assumed to follow a non-homogeneous Poisson process with piecewise-constant intensity functions. We propose a Dirichlet process mixture model to accommodate heterogeneity in subject-specific change-points. The proposed approach provides an objective way of clustering subjects based on the change-points without the need of pre-specified number of latent clusters or model selection procedure. A simulation study shows that the proposed model outperforms the existing Bayesian finite mixture model in detecting the number of latent classes. The simulation study also suggests that the proposed method is robust to the violation of model assumptions. We apply the proposed methodology to the Naturalistic Teenage Driving Study data to assess the change in driving risk and detect subgroups of drivers.