Heterogeneous vehicle routing problem with time windows (HVRPTW) aspect of hazardous material (HazMat) transportation is studied in this article. Given the multiobjective nature of HazMat transportation, a three-objective optimization model is defined for HVRPTW in HazMat transportation. The objective is to determine fleet size and routes so as to meet all given constraints as well as to minimize the objectives of the total traveling cost, the transportation risk, and the average vehicle redundancy. A load-variant HazMat transportation risk assessment model considering vehicle type and waiting time is presented to describe the transportation risk. A variable neighborhood search-based hybrid multiobjective evolutionary algorithm (VN-HMOEA) is proposed for solving the problem. The proposed VN-HMOEA integrates a two-phase push forward insertion heuristic (TP-PFIH) for initial population construction, specialized evolutionary operators for optimizing different objectives and a VNS metaheuristic for local search exploitation. The algorithm is tested on the modified Solomon benchmark instances for HVRPTW. Experimental results show that the proposed VN-HMOEA is competitive in terms of convergence and diversity. We also find that multiobjective fashion is of great significance for transportation risk mitigation to provide a set of nondominated solution rather than a single solution.