The OFEX (Optimal and Fully EXplicit) rate controller is able to provide not only the optimal bandwidth allocation but also the fully explicit congestion signal to sources. It feeds back the congestion signal from the most congested link along a flow path, instead of the summation of congestion signals. The OFEX controller overcomes the drawbacks of the relatively explicit controllers that (1) bias the multi-bottlenecked users in terms of the source sending rate and convergence speed, (2) are not adaptable to varying link bandwidth and (3) can potentially incur large queue sizes upon congestion. In this paper, we would like to investigate the convergence property of the OFEX controller which is of particular concern and interests to researchers, and point out how the OFEX controller can quickly converge to equilibrium even under bandwidth variations. Furthermore, our OPNET simulation experimentally demonstrates the superior convergence capability of the OFEX controller when compared with other schemes.