The maximum probability path problem has been applied in many real fields. However, the problem of computing a path of maximum probability often is transformed into a shortest path problem so as to use suitably the existed shortest path algorithm such as Dijkstra's algorithm. We propose a new algorithm for maximum probability path problem, which is linear in size of a system and does not need to transform. The algorithm mainly exploits probability-first strategy, a probability ordered queue and some FIFO (First In First Out) queues. We prove our algorithm's soundness and completeness with respect to optimal probability problem, and take project application as an example to show our algorithm's application.