Hazardous material transportation is well-known for its high potential risk. Minimizing the transportation risk is an important issue for hazardous material transportation. This paper focuses on a novel algorithm for the hazardous material transportation problem via lane reservation, whose goal is to obtain a best compromise between the impact on normal traffic due to lane reservation and the transportation risk. Firstly, a bi-objective integer programming model for the considered problem is formulated and transformed into a series of single objective models by\varepsilon-constraint method. For the transformed single objective models, a cut-and-solve and cutting plane combined method is proposed to reduce the computational time. The performance of the proposed algorithm is evaluated by an instance using a real network topology and randomly generated instances. Computational results demonstrate that the cut-and-solve and cutting plane combined method runs faster than direct use of software package CPLEX.