The exploding growth of World Wide Web applications in recent years has overwhelmed the internet with multimedia traffic. A future performance concern is to keep pace with the quickly growing bandwidth requirements. IP over ATM is a way to relax such requirements. It provides a hybrid approach to support both layer 3 software forwarding and layer 2 ATM hardware switching. A switched virtual connection may be suitable for traffic involving large data transfers and QoS provision like Guarantee Service (GS) applications. In the hybrid IP/ATM networks, the packet-level instead of the cell-level behavior is the relevant measure of performance. In this paper, we propose a so-called Frame-based Priority Scheduling (FBPS) algorithm for GS applications. FBPS focuses on the packet-level performance while transmitting based on cells. The most attractive feature of FBPS is its simplicity. We provide a systematic analysis of FBPS scheduler and derive the bound on its fairness when the flow traffic is shaped by a leaky bucket. It shows the FBPS is competitive with certain complex scheduling disciplines such as PGPS. We also verify our analytical bounds by simulation.