One of the main challenges in video transmission is understanding and adapting to the varying network bandwidth. The traditional approach of bandwidth estimation is not accurate as there are many factors like congestion that can delay the arrival rate of the ping packet which may lead to a misconception that the bandwidth was low. Thus, the better approach to this problem will be to estimate the link conditions based on the buffer fullness. In this paper, a new system to support streaming of live and stored video through wireless network is proposed which is based on adaptive playback buffer management on the top of HTTP at the client. The buffer fullness is treated as a direct state variable that reflects the fluctuation of the network bandwidth. The buffer fullness estimation predicts the buffer status at a point in the future based on observations of the buffer over a stipulated period of time. The proposed algorithm uses non-linear exponential non-parametric regression for computing the decision parameter. A feedback message is then sent to the server in order to change the quality of the video stream for smoother video play at the client side. The synchronized update and feedback between the server and clients is achieved using HTTP protocol. During the experimentation with live video streaming, the proposed algorithm shows an improvement of 24.48% in average peak signal-to-noise ratio and 6.63% in average structural similarity index against the buffer underflow probability algorithm.