Betweenness centrality (BC) is an important graph analytical application for large-scale graphs. While there are many efforts for parallelizing betweenness centrality algorithms on multi-core CPUs and many-core GPUs, in this work, we propose a novel fine-grained CPU-GPU hybrid algorithm that partitions a graph into CPU and GPU partitions, and performs BC computations for the graph on both the CPU and GPU resources simultaneously with very small number of CPU-GPU communications. The forward phase in our hybrid BC algorithm leverages the multi-source property inherent in the BC problem. We also perform a novel hybrid and asynchronous backward phase that performs minimal CPU-GPU synchronizations. Evaluations using a large number of graphs with different characteristics show that our hybrid approach gives 80% improvement in performance, and 80-90% less CPU-GPU communications than an existing hybrid algorithm based on the popular Bulk Synchronous Paradigm (BSP) approach.