Large Language Models (LLMs) demonstrate superior performance in generative scenarios and have attracted widespread attention. Among them, stylized dialogue generation is essential in the context of LLMs for building intelligent and engaging dialogue agent. However the ability of LLMs is data-driven and limited by data bias, leading to poor performance on specific tasks. In particular, stylized dialogue generation suffers from a severe lack of supervised data. Furthermore, although many prompt-based methods have been proposed to accomplish specific tasks, their performance in complex real-world scenarios involving a wide variety of dialog styles further enhancement. In this work, we first introduce a stylized dialogue dataset StyleEval with 38 styles by leveraging the generative power of LLMs comprehensively, which has been carefully constructed with rigorous human-led quality control. Based on this, we propose the stylized dialogue framework StyleChat via recitation-augmented memory strategy and multi-task style learning strategy to promote generalization ability. To evaluate the effectiveness of our approach, we created a test benchmark that included both a generation task and a choice task to comprehensively evaluate trained models and assess whether styles and preferences are remembered and understood. Experimental results show that our proposed framework StyleChat outperforms all the baselines and helps to break the style boundary of LLMs.