Blind image deblurring aims at recovering a clean image from the given blurry image without knowing the blur kernel. Recently proposed dark and extreme channel priors have shown their effectiveness in deblurring various blurry scenarios. However, these two priors fail to help the blur kernel estimation under the particular circumstance that clean images contain neither enough darkest nor brightest pixels. In this paper, we propose a novel and robust non-linear channel (NLC) prior for the blur kernel estimation to fill this gap. It is motivated by a simple idea that the blurring operation will increase the ratio of dark channel to bright channel. This change has been proved to be true both theoretically and empirically. Nonetheless, the presence of the NLC prior introduces a thorny optimization model. To handle it, an efficient algorithm based on projected alternating minimization (PAM) has been established which innovatively combines an approximate strategy, the half-quadratic splitting method, and fast iterative shrinkage-thresholding algorithm (FISTA). Extensive experimental results show that the proposed method achieves state-of-the-art results no matter when it has been applied in synthetic uniform and non-uniform benchmark datasets or in real blurry images.