Searching for the longest common subsequence (LCS) of biosequences is one of the most important problems in bioinformatics. A fast algorithm for LCS problem FAST_LCS is presented. The algorithm first seeks the successors of the initial identical character pairs according to a successor table to obtain all the identical pairs and their levels. By tracing back from the identical character pair at the highest level, strong pruning rules are developed. For two sequences X and Y with length n and m, respectively, the memory required for FAST_LCS is max{4*(n+1)+4*(m+1), L}, where L is the number of identical character pairs. The time complexity of parallel computing is O(|LCS(X,Y)|), where |LCS(X,Y)| is the length of the LCS of X,Y. Experimental result on the gene sequences of tigr database using MPP parallel computer Shenteng 1800 shows that our algorithm can find the exact solutions significantly more efficiently than other LCS algorithms.