Recent years have witnessed a digital explosion in the deployment of 5G and the proliferation of 5G-enabled innovations. Compared with 5G, 6G is envisioned to achieve a much higher performance and experience a number of paradigm shifts, such as exploiting new spectrum, applying ubiquitous machine learning and Artificial Intelligence (ML/AI) technologies and building a space-air-ground-sea integrated network. However, these paradigm shifts may lead to numerous new security and privacy issues, that traditional security measures may not be able to address. Moreover, the expected high performance of 6G also challenges network reliability and energy efficiency. To tackle these issues and build a trustworthy 6G network, we introduce a novel trust framework called SIX-Trust. This framework is composed of three layers with an emphasis on distinct aspects: sustainable trust (S-Trust), with a particular focus on trust in applications of AI, novel trust evaluation methods and modeling of trust relationships; infrastructure trust (I-Trust), which is more focused on the trustworthiness of network infrastructure; and xenogenesis trust (X-Trust) paying special attention to the core technologies which form the backbone of 6G trust. Besides, the importance of each layer varies under different application scenarios of 6G. For each layer, we briefly introduce its related enabling technologies, and demonstrate how these technologies can be applied to enhance the trust and security of the 6G network. Finally, a use case is illustrated and analyzed. In general, SIX-Trust provides a holistic framework for defining and modeling trust in 6G, which can facilitate establishment of a trustworthy 6G network.