Recent approaches for empathetic response generation mainly focus on emotional resonance and user understanding, without considering the system's personality. Consistent personality is evident in real human expression and is important for creating trustworthy systems. To address this problem, we propose StyEmp, which aims to stylize the empathetic response generation with a consistent personality. Specifically, it incorporates a multi-grained prefix mechanism designed to capture the intricate relationship between a system's personality and its empathetic expressions. Furthermore, we introduce a personality reinforcement module that leverages contrastive learning to calibrate the generation model, ensuring that responses are both empathetic and reflective of a distinct personality. Automatic and human evaluations on the EMPATHETICDIALOGUES benchmark show that StyEmp outperforms competitive baselines in terms of both empathy and personality expressions.