This article presents an efficient parametric optimization method for the biobjective optimal routing problem. The core process is a bounded greedy single-objective shortest path approximation algorithm. This method avoids the computationally intensive dominance check with labeling methods and overcomes the deficiency with existing parametric methods that can only find extreme nondominated paths. Moreover, we propose a decomposition scheme to convert a multiobjective routing problem into a number of biobjective problems. We then compare its computational performance against the classic label-correcting method over a set of synthetically generated random networks and illustrate its algorithmic advances and solution behaviors by an example application of routing hazardous materials in a U.S. northeastern highway network.