Large Language Models (LLMs) demonstrate a remarkable ability to comprehend human instructions and generate high-quality text. This capability allows LLMs to function as agents that can emulate human beings at a more sophisticated level, beyond the mere replication of basic human behaviours. However, there is a lack of exploring into leveraging LLMs to craft characters from diverse aspects. In this work, we introduce the Customisable Conversation Agent Framework, which leverages LLMs to simulate real-world characters that can be freely customised according to various user preferences. This adaptable framework is beneficial for the design of customisable characters and role-playing agents aligned with human preferences. We propose the SimsConv dataset, which encompasses 68 different customised characters, 1,360 multi-turn role-playing dialogues, and a total of 13,971 interaction dialogues. The characters are created from several real-world elements, such as career, aspiration, trait, and skill. Building upon these foundations, we present SimsChat, a freely customisable role-playing agent. It incorporates diverse real-world scenes and topic-specific character interaction dialogues, thereby simulating characters' life experiences in various scenarios and topic-specific interactions with specific emotions. Experimental results indicate that our proposed framework achieves desirable performance and provides a valuable guideline for the construction of more accurate human simulacra in the future. Our data and code are publicly available at https://github.com/Bernard-Yang/SimsChat.