Polarimetric imaging has prominent advantages in scattering media. Emerging learning-based polarimetric technologies has succeeded but heavily relied on paired data corresponding to the same scenes. In this paper, we propose an unsupervised method for the unpaired underwater-image recovery with a polarimetric generative adversarial network, named U2R-pGAN. The method breaks the dependence on strictly paired images in traditional learning-based methods and significantly enhances the restoration performance. Besides, we merge polarization losses into the network, which has been verified beneficial for details restoration. Imaging experiments have been devised and performed on different objects and viewing conditions under varying turbidity. The results demonstrate that the proposed method improves the peak signal to noise ratio by an average of 3.4 dB. The new method can be readily applied to practical underwater applications.