Dynamic Adaptive Streaming over HTTP (DASH) is a technology in which the client is served by requesting the next media segments of appropriate quality. The client measures the current available bandwidth on the basis of the data transmission rate of the previous media segments. To obtain the best quality without generating buffering, it is necessary to accurately measure the available bandwidth. However, the traditional available bandwidth measurement is unsuitable for a DASH system. Because this method does not consider TCP slow-start characteristics, the accuracy is lowered. Furthermore, the segment size varies greatly according to the quality, and measurement of the available bandwidth impact is different for each size of the segment. As a result, the difference in the measured available bandwidth according to the size of the previous media segment can reduce the user Quality of Experience (QoE) such as the selection of incorrect quality and unwanted changes in the quality. In this paper, a new DASH bandwidth measurement method is proposed to reduce the error when measuring the available bandwidth due to a TCP slow start by excluding the section of the TCP slow start from the measurement of the available bandwidth. The proposed method can address the problem that results when the measurement of the available bandwidth differs according to the previous segment size. We implement our proposed available-bandwidth measurement method in an open-source-based DASH system and compare its performance to the traditional method. From the results of the performance evaluation, the available bandwidth measurement accuracy is improved by approximately 20% compared with the traditional method. In addition, we confirmed that the user QoE is improved in terms of the average quality of service and the number of changes in the quality of the segment.