To guarantee Quality of Experience (QoE) for video streaming services in a future Internet architecture, Content Centric Network (CCN), Dynamic Adaptive Streaming via HTTP (DASH) technology is used to deliver the proper video content according to the network situation. However, CCN enables a host-to-content communication model and has a universal caching design, which seriously decreases the performance of DASH over CCN. In this paper, we propose a hop-by-hop adaptive video streaming scheme (HAVS-CCN) to improve the performance of adaptive video streaming in CCN. HAVS-CCN is simple and applicable to be deployed on DASH over CCN. It directly adjusts video quality and solves network congestion at the bottleneck of transmission path when DASH inaccurately estimates the network throughout. Our scheme optimizes the hop-by-hop content transmission, which achieves video quality adaption and data packet flow control simultaneously. Simulation results, on small-scale networks and large-scale networks, reveal that DASH with HAVS-CCN scheme outperforms the original DASH over CCN, in terms of video playback quality and average delay.