We propose an efficient bandwidth estimation method to wireless networks. In the proposed method, the available bandwidth (AB) is estimated based on a packet pair probing technique (PPPT) that is a well-known mechanism for measuring the capacity of an end-to-end path without any information of network routers. To adapt the PPPT to the wireless network, in this paper, the cross traffic and the capacity variation of wireless link are considered to estimate the AB. We also introduce a video streaming application using the estimated AB. Experimental results show that the proposed method does not only estimate the accurate bandwidth, but also improve the performance of video streaming application over wireless networks.