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This paper considers planning a UAV trajectory when the UAV collects data for ground access points (APs), aiming to minimize the overall UAV power consumption in executing the data-collection tasks. We explore to achieve this by selecting an optimal data rate for each hovering point of the UAV when it communicates with the ground APs. Specifically, we mainly consider the UAV power consumption caused by traveling, hovering, and communications with APs. Appropriate data rates can reduce the communication and data collection time and thus can reduce the hovering and communication power consumption. Regarding this, we propose an integer linear programming (ILP) model which minimizes the total UAV power consumption by selecting optimal data rates for different hovering points.