Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected weighted graph with vertices and edges. This algorithm uses the cluster techniques to reduce the number of processors by fraction and the parallel work by the fraction O ( ), where is an arbitrary function. In the case , the algorithm runs in logarithmic-time and use super linear work on EREWPRAM model. In general, the proposed algorithm is the simplest one.