This paper aims to exploit the full potential of gradient-based methods, attempting to explore a simple, robust yet discriminative image prior for blind deblurring. The specific contributions are three-fold: Above all, a pure gradient-based heavy-tailed model is proposed as a generalized integration of the normalized sparsity and the relative total variation. On the second, a plug-and-play algorithm is deduced to alternatively estimate the intermediate sharp image and the nonparametric blur kernel. With the numerical scheme, image estimation is simplified to an image smoothing problem. Lastly, a great many experiments are performed accompanied with comparisons with state-of-the-art approaches on synthetic benchmark datasets and real blurry images in various scenarios. The experimental results show well the effectiveness and robustness of the proposed method.