Polarimetric imaging is an effective way for clear vision in water, in which deducing the object radiance in clear water from the obtained polarimetric information in turbid water is essential. In this letter, we propose, for the first time to our knowledge, a learning-based method for polarimetric underwater image recovery. It is based on the dense network and can learn well the relation between the object radiance and the polarization information. The experimental results demonstrate that additionally introducing the polarization information is beneficial for improving the image quality. Moreover, the proposed learning-based method can effectively remove the veiling light and outperforms other existing methods, even in dense turbid water.