In this paper, the Double Shortest Arborescence & Merging method is presented as an efficient heuristic algorithm for the Public Vehicle Routing Problem which is to find the minimum total cost routes of M or less vehicles to traverse the required arcs(demand streets) at least once and return to their starting depot on a directed network. Double Shortest Arborescence which consists of forward shortest aborescence and backward one informs M or less shortest routes to traverse all required arcs. The number of these routes is reduced to M or less by merging routes. The computational experiment based on randomly generated networks reports that this algorithm is efficient.