Disaster rescue needs rapid transportation of both supplies and staff. The abrupt disasters often affect the traffic states, and research on the real-time fastest path under dynamic road conditions has important economic and social values. Aiming at dealing with the abrupt and frequent road variation after disaster, a fast algorithm of real-time Fastest Traffic Path(ARFTP) is proposed, which reduces the amount of re-calculation on the nodes and the sub-paths by classifying the nodes into different types and filtering them, then putting them into corresponding calculation modules, so as to avoid redundant calculations. When the vehicles are on the original shortest path to the disaster area and receive real-time road variation information, the up-to-date fastest shortest path can be calculated by ARFTP rapidly. Experiments have been made to test the correctness and efficiency of ARFTP with many cases of road cases, and the results proved its effect in improving the efficiency which has some guidance significance to disaster relief transportation.