The demand for satellite communication is increasing to provide connectivity in areas without terrestrial network coverage. Specifically, multibeam low-Earth orbit (LEO) satellite communication is emerging as a key solution to providing high-capacity, wide-area coverage to remote regions such as oceans, mountains, and deserts. In this paper, an opportunistic resource scheduling scheme is analyzed to efficiently utilize LEO satellite resources. An opportunistic resource scheduling algorithm is proposed that optimally allocates and schedules based on the time-varying channel conditions of each user. Moreover, the proposed algorithm is designed to maximize total average capacity while satisfying the minimum capacity requirement for each user, thereby ensuring user-specific quality of service (QoS). An algorithm utilizing a Lagrangian dual approach was developed to find the optimal beam allocation. The simulation results demonstrate that the proposed algorithm achieves capacity convergence while satisfying the QoS requirements of all users.