In the process of hazardous material transportation, the risk is a significant factor that should be considered due to the potential severe consequence of an incident. Regardless of risks, time is a paramount concern that should be considered in hazardous material transportation. In this way, this paper introduces a bi-objective model for a vehicle routing and scheduling problem of hazardous material distribution problems under the fuzzy condition to minimize both total distribution time and risks. In the proposed model, the fuzzy inference system and fuzzy failure mode and effects analysis are applied to identify and calculate the high-level risks instead of the previous simple methods for the first time. Moreover, Jimenez method and fuzzy goal programming are respectively utilized to convert the fuzzy bi-objective model into the same crisp and single-objective one. Besides, to cope with the NP-hardness of the large-sized problems, two meta-heuristic algorithms namely invasive weeds optimization and genetic algorithm is used, and several sensitivity analyses are performed to prove the efficiency of the proposed approach. The performance of the proposed algorithms is also assessed through a comparative study. Finally, the proposed model is implemented to a real case study to prove the validity of the model.