Given an undirected graph G(V,E), |V|=n,|E|=m. Based on SIMD shared memory model, a new parallel algorithm for computing connected components of graphs is proposed by using fast data transmission principle. As a result, the algorithm requires O(log²n) time and O(n²/logn) processors on SIMD-CREW shared memory model. But on SIMD-CRCW shared memory model, the algorithm only requires O (logn) time and O(n²) processors. To compare our algorithm with known Hirschberg s algorithm, there exists some differences. The major differences are identified as:1)the way to solve this problem is different;2)proposed algorithm is simple and easy to understan;3)proposed algorithm's implementation on some practical networks such as mesh-of-rtee has better time complexity.