A node ranking of a graph G = (V, E) is a proper node coloring C: V →⇔ such that any path in G with end nodes x, y fulfilling C(x) = C(y) contains an internal node z with C(z) > C(x). In the on-line version of the node ranking problem, the nodes v1, v2,..., vn are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v1, v2,..., vi}] are known when the color for the node vi be chosen. And the assigned color can not be changed later. In this paper, we present a parallel algorithm to find an on-line node ranking for general tree. Our parallel algorithm needs O(nlog2n ) time with using O(n3 / log2n) processors on CREW PRAM model. [ABSTRACT FROM AUTHOR]