Small-cell network is a promising solution to high video traffic. However, with the increasing number of devices, it cannot meet the requirements from all users. Thus, we propose a caching device-to-device (D2D) scheme for small-cell networks, in which caching placement and D2D establishment are combined. In this scheme, a limited cache is equipped at each user, and the popular files can be prefetched at the local cache during off-peak period. Thus, dense D2D connections can be established during peak time aided by these cached users, which will reduce the backhaul pressure significantly. To do this, first, an optimal caching scheme is formulated according to the popularity to maximize the total offloading probability of the D2D system. Thus, most edge users can obtain their required video files from the caches at users nearby, instead from the small-cell base station. Then, the sum rate of D2D links is analyzed in different signal-to-noise ratio (SNR) regions. Furthermore, to maximize the throughput of D2D links with low complexity, three D2D-link scheduling schemes are proposed with the help of bipartite graph theory and Kuhn-Munkres algorithm for low, high and medium SNRs, respectively. Simulation results are presented to show the effectiveness of the proposed scheme.