In ITS environment, the driver-assistant services usually demand delivering video content to vehicular users, which is very useful in the intervention of emergency services, and reminds the drivers the traffic jam in ahead road. Nowadays for online video delivery in connected vehicle networks, HTTP adaptive streaming (HAS) is one of the most promising technologies, where a video is encoded into multiple bitrates and then split into small segments. It is crux for ITS service providers how to improve users' QoE through an adaptive video segments request strategy. From the perspective of adaptive matching among segment bitrate, network bandwidth, and buffer occupancy, we propose a bandwidth-aware video segment request strategy to optimize user's QoE (for short Bw-QoE), which consists of two parts, i.e., available bandwidth estimation, and segment's bitrate selection. First, based on the severity of bandwidth fluctuation, Bw-QoE estimates the available bandwidth with different historical weighted average methods. Then constrained by the estimated available bandwidth and buffer occupancy, the adaptive bitrate selection is formulated as an optimization model to maximize user's QoE of a video streaming session. It is fairly attractive for Bw-QoE to prevent buffer overflow, underflow and unuseful download, and to reduce bitrate switching. Compared with the classic strategy (e.g., LIU's strategy), the simulation results show that the proposed strategy Bw-QoE has higher average video bitrate (about 8%-10%), less interruption (about 100%), less segment bitrate switching (about 15%-17%) and higher buffer occupancy (about 13%-51%), which demonstrate that our strategy effectively improves QoE.