Safety of the hazardous chemicals road transportation system (HCRTS) is an important, complex, social, and environmental sensitive problem. The complexity, dynamics, and multi-link features of HCRTS have made it necessary to think beyond traditional risk analysis methods. Based on the relevant literature, Functional Resonance Analysis Method (FRAM) is a relatively new systemic method for modeling and analyzing complex socio-technical systems. In this study, a methodology that integrates FRAM, fuzzy sets, and risk matrix is presented to quantitatively assess the risks factors representing failure function links in HCRTS. As the strength of function links can be illustrated by the RI (risk index) of risk factors identified in failure function links, 32 risk factors representing 12 failure function links were first identified by accident causes analysis and the framework of FRAM. Fuzzy sets were then utilized to calculate the weight of the likelihood and consequence of the risk factors. Finally, according to the assessment results of the identified risk factors by a two-dimensional risk matrix, the weaker function links in the whole HCRTS chain were identified. HCs road companies, regulatory authorities, relevant practitioners, and other stakeholders should pay more attention to these links.