We present a new linear algorithm for coloring the edges of a tree. Although this is not the first linear algorithm for the problem, our algorithm unlike the existing ones can be parallelized directly. The parallelization is obtained by showing that edge-coloring can be carried out using tree contraction. Hence, it can be done in O(log n) time using n/logn processors on the EREW PRAM. When the problem is extended to one of coloring the edges of a graph with edge-disjoint cycles, the said algorithm for trees can be extended very easily without increasing the resource requirement.