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Video streaming application such as YouTube is one of the most popular mobile applications. To adjust the quality of video for available network bandwidth, a streaming server provides multiple representations of video of which bit rate has different bandwidth requirements. A streaming client utilizes an adaptive bit rate scheme to select a proper video representation that the network can support. The download behavior of video streaming client player is governed by several parameters such as maximum buffer size. Especially, the size of the maximum playback buffer in the client player can greatly affect the user experience. To tackle this problem, in this paper, we propose the maximum buffer size optimization according to available network bandwidth and buffer status. Our simulation study shows that our proposed buffer size optimization scheme successfully mitigates playback stalls while preserving the similar quality of streaming video compared to existing ABR schemes.