An important index widely used to analyze social and information networks is betweenness centrality. In this paper, given a dynamic and directed graph G and a vertex r in G, we present the DyBED algorithm that updates the (approximate) betweenness centrality of r, when an update operation (vertex/edge insertion/deletion) occurs in G. Our algorithm first during pre-processing computes two subsets of the vertex set of G, called ΠT(r) and ΠT(r). The Cartesian product of these two sets defines the sample space of our algorithm. In other words, each sample is a pair, whose first element belongs to ΠT(r) and second element belongs to ΠT(r). Then after each update operation, DyBED updates the sets ΠT(r) and ΠT(r), the sampled pairs, the information stored for each sample and accordingly, the betweenness centrality of r. We theoretically and empirically evaluate DyBED and show that it yields significant improvement over existing work. In particular, our extensive experiments reveal that DyBED is orders of magnitude faster than most efficient existing algorithms.