This paper proposes a novel video delivery scheme that reduces the bandwidth consumption cost from a video server to terminals in Long-Term Evolution networks. This proposed scheme combines optimized hybrid multicast with a segment-based caching strategy for use in environments where the maximum number of multicast channels is limited. The optimized hybrid multicast, allocation of multicast channels, and cache allocation are determined on. the basis of a video's request rate, the related video's length, and the variable cost per unit size of a segment belonging to the related video. Performance evaluation results show that the proposed scheme reduces a video's delivery costs. This work is applicable to on-demand TV services that feature asynchronous video content requests.