In this paper, using the BSP/CGM model, we propose a parallel algorithm and implement it on a GPGPU to obtain a minimum spanning tree of a graph. Previous works for this problem are based on the solution of the list ranking problem which, though efficient in theory, did not produce good speedups in practice. In a later work, based on the idea of computing a structure called strut, we proposed a parallel algorithm under the BSP/CGP model to obtain a minimum spanning tree without using list ranking. It is based on the construction of an auxiliary bipartite graph and uses integer sorting. In this paper, we improve that work in some aspects. The proposed algorithm does not require the computation of the bipartite graph, and the strut construction does not require the sorting algorithm. The efficiency and scalability of the proposed algorithm are verified through experimental results obtained by an implementation on GPGPU.