The dynamic response of a cup anemometer is studied, based on an equation of motion. Torque acting on the anemometer is shown to be different in the accelerating and the decelerating states of rotation. The values of the coefficients in the equation of motion are also different. They can be determined by simple experiments. The fluctuation of natural wind measured by a cup anemometer is compared with that observed by a sonic anemometer as a reference sensor. A new reduction method for a cup anemometer record for fluctuating wind is proposed and tested.