Alpha-Beta search is an important heuristic technique used in pruning a game tree. Recently, parallelism has been introduced to further improve the efficiency of heuristic searches, including Alpha-Beta search. This paper presents a new parallel Alpha-Beta search algorithm that applies prioritizing scheme. To verify its performance, we implemented the algorithm on Sequent Symmetry shared memory multiprocessor system. Our experimental results show that for the best ordering uniform trees, we are able to obtain a consistent speedup of a linear order to the number of processors used. An overall speedup with random node ordering isillustrated. The paper concludes with some characteristics of the Alpha-Beta search that make the application of priorities suitable for its corresponding parallel algorithm.