An H-infinity based robust controller is designed for a rate-feedback flow-control problem in single-bottleneck communication networks. The controller guarantees stability robustness to uncertain time-varying multiple time-delays in different channels. It also brings the queue length at the bottleneck node to the desired steady-state value asymptotically and satisfies a weighted fairness condition. Lower bounds for stability margins for uncertainty in the time-delays and for the rate of change of the time-delays are derived. A number of simulations are included to demonstrate the time-domain performance of the controller. Trade offs between robustness and time-domain performance are also discussed.