Abstract We present a fast parallel algorithm running in O(log' n) time on a CREW PRAM with O(n) proces-sors for finding the kth longest path in a given tree of n vertices (with O(n2) intervertex distances). Our algorithm is obtained by eficient parallelization of a sequential algorithm which is a ' variant of both Megiddo et al' s algorithm [1.2] and Fredrickson et al' s algorithm [S] based on centroid decompositibn of tree land suc-cinct representation of the set of' intervertex distances.' With the same time and space bound as the best known reszdlt, our sequential algorithm maintains a shorter length of the decomposition tree.