Dynamic adaptive streaming over Hypertext Transfer Protocol (HTTP) is an advanced technology in video streaming to deal with the uncertainty of network states. However, this technology has one drawback as the network states frequently and continuously change. The quality of a video streaming fluctuates along with the network changes, and it might reduce the quality of service. In recent years, many researchers have proposed several adaptive streaming algorithms to reduce such changes. However, these algorithms only consider the current state of a network. Thus, these algorithms might result in inaccurate estimates of a video quality in the near term. Therefore, in this paper, we propose a method using fuzzy logic and a mathematics moving average technique, in order to reduce mobile video quality fluctuation in Dynamic Adaptive Streaming over HTTP (DASH). First, we calculate the moving average of the bandwidth and buffer values for a given period. On the basis of differences between real and average values, we propose a fuzzy logic system to deduce the value of the video quality representation for the next request. In addition, we use the entropy rate of a bandwidth measurement sequence to measure the predictable/stabilization of our method. The experiment results show that our proposed method reduces video quality fluctuation as well as improves 40% of bandwidth utilization compared to existing methods.