Ethernet Passive Optical Networks (EPONs) are not only cost-effective, but also provide high throughput, high bandwidth utilization, and low transmission latency. As a result, EPONs are a viable solution for overcoming the bandwidth bottleneck problem in local access networks. This study develops a novel Dynamic Bandwidth Allocation (DBA) scheme, designated as Frame-oriented Interleaved Polling with Adaptive Cycle Time (FIPACT), to provide a differentiated Quality-of-Service (QoS) capability in EPONs. FIPACT adopts a framed approach, in which the upstream network bandwidth is partitioned into successive frames. Within each frame, each Optical Network Unit (ONU) is guaranteed the network resources necessary to transmit a specific quota of Voice over Internet Protocol (VoIP), video, and Internet access traffic, respectively. Since FIPACT permits these three types of traffic stream to share the available bandwidth efficiently whilst still satisfying their respective QoS requirements, it provides an effective means of achieving differentiated triple-play services in EPONs. The simulation results demonstrate the effectiveness and efficiency of the proposed approach.