Betweenness centrality is essential in complex network analysis; it characterizes the importance of nodes and edges in networks. It is a crucial problem that exactly computes the betweenness centrality in large networks faster, which urgently needs to be solved. We propose a novel algorithm for betweenness centrality based on the parallel computing of adjacency matrices, which is faster than the existing algorithms for large networks. The time complexity of the algorithm is only related to the number of nodes in the network, not the number of edges. Experimental evidence shows that the algorithm is effective and efficient. This novel algorithm is faster than Brandes' algorithm on small and dense networks and offers excellent solutions for betweenness centrality index computing on large-scale complex networks.