Speech-driven 3D motion synthesis seeks to create lifelike animations based on human speech, with potential uses in virtual reality, gaming, and the film production. Existing approaches reply solely on speech audio for motion generation, leading to inaccurate and inflexible synthesis results. To mitigate this problem, we introduce a novel text-guided 3D human motion synthesis method, termed T3M. Unlike traditional approaches, T3M allows precise control over motion synthesis via textual input, enhancing the degree of diversity and user customization. The experiment results demonstrate that T3M can greatly outperform the state-of-the-art methods in both quantitative metrics and qualitative evaluations. We have publicly released our code at https://github.com/Gloria2tt/naacl2024.git