Global Routing (GR) is a critical step in the VLSI design process. With the ever increasing number of components on a single chip, there is great need of better routing algorithms to produce efficient, congestion free routing. We propose a hybrid Biogeography-based Optimization (BBO)/Maze Routing (MR) algorithm which focuses on producing zero overflow routing solutions. MR is used to generate initial routing of all nets and then a novel BBO based routing algorithm is used to iteratively perform the Rip-up and Reroute (R&R) of congested nets. Lower and upper bounds on the 3D wirelength were computed using the 2-D routing solution generated by the proposed algorithm. The performance of the proposed router was evaluated on ISPD 2007 benchmarks and the results were found to be comparable with some of the state-of-the-art academic global routers and considerably less total overflow was achieved.