In recent years, HTTP adaptive streaming (HAS) has attracted considerable attention as the state-of-the-art technology for video transport. HAS dynamically adjusts the quality of video streaming according to the network bandwidth and device capability of users. Content-Centric Networking (CCN) has also emerged as a future Internet architecture, which is a novel communication paradigm that integrates content delivery as a native network primitive. These trends have led to the new research issue of harmonizing HAS with the in-network caching provided by CCN routers. Previous research has shown that the performance of HAS can be improved by using the H.264/SVC(scalable video codec) in the in-network caching environments. However, the previous study did not address the misbehavior that causes video freeze when overestimating the available network bandwidth, which is attributable to the high cache hit rate. Thus, we propose a new SVC-based adaptation algorithm that utilizes a drop timer. Our approach aims to stop the downloading of additional enhancement layers that are not cached in the local CCN routers in a timely manner, thereby preventing excessive consumption of the video buffer. We implemented our algorithm in the SVC-HAS client and deployed a testbed that could run Smooth-Streaming, which is one of the most popular HAS solutions, over CCNx, which is the reference implementation of CCN. Our experimental results showed that the proposed scheme (SLA) could avoid video freeze in an effective manner, but without reducing the high hit rate on the CCN routers or affecting the high video quality on the SVC-HAS client.