The fast piezo-driven scanner (FPDS) compensates for vibrations in the unmanned aerial vehicle (UAV) image stabilization system. However, the hysteresis nonlinearity reduces the positioning accuracy of the FPDS. To address this challenge, this paper presents a novel weighted polynomial modified Bouc–Wen (WPMBW) model cascaded with a linear dynamic model to describe counterclockwise, asymmetric, and rate-dependent hysteresis loops of an FPDS. The proposed approach utilizes the weighted polynomial function to describe the asymmetric characteristic and the linear dynamic model to capture the rate-dependent behavior. By modifying the last two terms in the classical Bouc–Wen (CBW) model, the modified BW model directly characterizes the counterclockwise hysteresis loops with fewer parameters, circumventing the algebraic-loop problem that arises in the inverse CBW model. The pseudorandom binary sequence (PRBS) input is employed to decouple the linear dynamic model from the WPMBW model. The sinusoidal input is then applied to stimulate the hysteresis phenomenon, and the parameters of the WPMBW model are estimated by the particle swarm optimization (PSO) toolbox. Experimental results on a commercial FPDS show that the proposed model is superior to the CBW and traditional asymmetric BW models in modeling accuracy and feedforward hysteresis compensation.