In multi-group multicast systems with greedy scheduling and quality-based channel state information feedback (QCF), a novel scheme to determine group-specific QCF thresholds is proposed for non-identical Rayleigh fading channels. Unlike the conventional schemes using a single common QCF threshold, the proposed scheme using group-specific QCF thresholds provides a trade-off between system capacity and fairness. Hence, it can enhance the fairness for multicast groups at the cost of system capacity. We analyze the capacity, fairness, and feedback overhead of the multi-group multicast systems with greedy scheduling and group-specific QCF to validate the effectiveness of the proposed scheme.