This paper proposes a utility function-based scheduling algorithm for integrated real-time and non-real-time services in long-term evolution systems. The proposed utility function satisfies the target dropping ratio of real-time users; it uses the delay constraint and increases the throughput of non-real-time users by scheduling real-time users together with non-real-time users. Simulation results show that the proposed scheduling algorithm significantly improves the throughput of non-real-time users without sacrificing the quality of service of real-time users.