This article presents an efficient optimal algorithm for virtual path (VP) bandwidth allocation in telecommunication networks. Given the network topology, link capacity, routes of VP offered traffic and the condition that only one shortest VP could be chosen for each source-destination pair (single-VP), the algorithm is able to optimize the allocation of the bandwidth of VP in order to minimize the highest call blocking probability (CBP) of all the source-destination pairs. Based on the results obtained from the test-bed networks, we compare the performance of the algorithm with that of another classical optimal algorithm - "bisection algorithm" - and conclude that the former is more efficient under the condition of single-VP.