The capacitated arc routing problem (CARP) is an important vehicle routing problem with numerous real world applications. In this paper, an extended version of CARP, the capacitated arc routing problem with priority edges is presented. The new introduced CARP is more general and closer to reality, and thus is more worthwhile to be solved. In this problem, a set of important priority edges is given and the task is to service of all edges with positive demand in such a way that the higher priority edges are visited as soon as possible. The capacitated arc routing problem with priority edges is an NP-hard problem, so we propose an algorithm that can quickly obtain optimal or near-optimal solution for the defined problem. Another important contribution is that our proposed algorithm is fast and easy to apply. In this paper, through some examples, efficiency of the proposed algorithm has been showed and some guidelines for the future studies have been given
