This paper proposes a capacity improving and energy saving scheduling scheme in push-based Converged Wireless Broadcasting and Cellular Network (CWBCN). We maximize the network capacity and alleviate request congestion through broadcasting/multi-casting the most popular services, and locally caching for further request on the user side. In the proposed scheme, we firstly introduce a UE (User Equipment)-based caching mechanism by considering both the frequency and recency of the popular services. Simulations show that the proposed mechanism brings a significant improvement on the capacity of the CWBCN. Based on the mechanism, a sleep-awake algorithm is proposed to further reduce the energy consumption of the UEs. Simulations show that with the proposed algorithm for the converged network can reduce 20%–30% energy consumption by comparing to the traditional one.