Polarimetric synthetic aperture radar (PolSAR) image classification has become a hot research topic in recent years. Sparse representation plays an important role in image processing. However, almost all the existing dictionary learning methods are linear transformation in the original data space, so they cannot capture the nonlinear relationship of the input data. The recently proposed projective dictionary pair learning (DPL) method has acquired good performance in classification result and time consumption. In this paper, we propose the nonlinear projective dictionary pair learning (NDPL) model, which introduced the nonlinear transformation to the DPL model. Our method can adaptively obtain the nonlinear relationship between the elements of input data, and it also has the excellent performance of DPL model. In this paper, we use three PolSAR images to test the performance of our proposed method. Compared with several state-of-the-art methods, our proposed method has obtained promising results in solving the task of PolSAR image classification.