We present Group Round-Robin (GRR) scheduling, a hybrid fair packet scheduling framework based on a grouping strategy that narrows down the traditional trade-off between fairness and computational complexity. GRR combines its grouping strategy with a specialized round-robin scheduling algorithm that utilizes the properties of GRR groups to schedule flows within groups in a manner that provides O(1) bounds on fairness with only O(1) time complexity. Under the practical assumption that GRR employs a small constant number of groups, we apply GRR to popular fair queuing scheduling algorithms and show how GRR can be used to achieve constant bounds on fairness and time complexity for these algorithms. We also present and prove new results on the fairness bounds for several of these fair queuing algorithms using a consistent fairness measure. We analyze the behavior of GRR and present experimental results that demonstrate how GRR can be combined with existing scheduling algorithms to provide much lower scheduling overhead and more than an order of magnitude better scheduling accuracy in practice than scheduling algorithms without GRR.