Recent years have witnessed a digital explosion with the deployment of 5G and proliferation of 5G-enabled innovations. Compared with 5G, 6G is envisioned to achieve much higher performance in terms of latency, data rate, connectivity, energy efficiency, coverage and mobility. To fulfil these expectations, 6G will experience a number of paradigm shifts, such as exploiting new spectrum, applying ubiquitous 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, which traditional security measures may not be able to deal with. To tackle these issues and build a trustworthy 6G network, we introduce a novel trust framework named as SIX-Trust, which composes of 3 layers: sustainable trust (S-Trust), infrastructure trust (I-Trust) and xenogenesis trust (X-Trust). Each layer plays a different role, and the importance of each layer varies for 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 trust and security of the 6G network. In general, SIX-Trust provides a holistic framework for defining and modeling trust of 6G, which can facilitate establishing a trustworthy 6G network.