In this paper, we focus on Universal Adversarial Perturbations (UAP) attack on state-of-the-art person re-identification (Re-ID) methods. Existing UAP methods usually compute a perturbation image and add it to the images of interest. Such a simple constant form greatly limits the attack power. To address this problem, we extend the formulation of UAP to a polynomial form and propose the Polynomial Universal Adversarial Perturbation (PUAP). Unlike traditional UAP methods which only rely on the additive perturbation signal, the proposed PUAP consists of both an additive perturbation and a multiplicative modulation factor. The additive perturbation produces the fundamental component of the signal, while the multiplicative factor modulates the perturbation signal in line with the unit impulse pattern of the input image. Moreover, we design a Pearson correlation coefficient loss to generate universal perturbations, for disrupting the outputs of person Re-ID methods. Extensive experiments on DukeMTMC-ReID, Market-1501, and MARS show that the proposed method can efficiently improve the attack performance, especially when the magnitude of UAP is constrained to a small value.