Data-Over-Cable Service Interface Specifications v1.1 (DOCSIS v1.1), developed for data transmissions over Hybrid Fiber Coaxial (HFC) networks, defines five upstream services for supporting per-flow Quality of Services (QoS). The cable modem termination system (CMTS) must periodically grant upstream transmission opportunities to the QoS flows based on their QoS parameters. However, packets may violate QoS requirements when several flows demand the same interval for transmission. This study proposes a two-phase, i.e., the scheduling sequence determination phase and the minislot assignment phase, minislot scheduling algorithm to reduce the QoS violation rate. In the scheduling sequence determination phase, the flow whose packets are most unlikely to violate QoS is scheduled first. Then, in the minislot assignment phase, the scheduler allocates to a flow the available interval where the likelihood of packet violation is minimum. Simulation results demonstrate that our scheduling algorithm can reduce the QoS violation rate by 80-35% over that of the first-come-first-serve-random-selection algorithm. It increases the utilization by 25% as well. The two-phase minislot scheduling algorithm can work within the DOCSIS v1.1 framework.