Aiming at the problem of low quality of video viewing experience in dynamic network environment with limited cache capacity, a Dynamic Adaptive Step-wise Bitrate Switching (DASBS) algorithm for HTTP streaming considering network bandwidth and cache capacity was proposed. Firstly, a sliding window was used to analyze the recent downloaded fragments, obtaining the initial bandwidth estimation. Then, according to the real-time bandwidth fluctuation degree and cache state, two correction factors were set to further smooth the bandwidth estimation. Finally, a cache threshold was set to establish a correlation with the current bitrate, and the bandwidth estimation and the cache dynamic threshold were used to jointly control the bitrate switching. Experimental results on platform libdash show that DASBS is better than Video Quality Control for QoE (VQCQ) algorithm in switching smoothness and its average bitrate of video playback is higher, which effectively improves the bandwidth utilization. Although the average bitrate is slightly lower than that of Evolution of Adaptive Bitrate Switching (EABS) algorithm, the number of switching times is greatly reduced, improving the switching stability. The experimental results show that the proposed algorithm has high bandwidth utilization, switching smoothness and switching stability in dynamic network environment, which can effectively improve user experience.