The objective of fastest completed vehicle routing problem (FCVRP) is to minimum complete time, this kind VRP problem was applied in emergency management and quick response supply chain management. Multiple ant colony algorithm for this problem is studied in this paper. The conception of FCVRP is given and then vehicle allocation method and objective function computing method are given to convert FCVRP problem to optimal alignment problem. At same time one local search method of this problem is introduced. Then learning multiple ant colony algorithm is bring forward to solve FCVRP and one numerical example is solved by this algorithm at last.