L₀ regularization is highly suitable for estimating the latent image in the blur kernel estimation step of the two-step process of blind image deblurring. To tackle L₀ regularization problem, the method randomly selects gradient truncation threshold or only depends on the experience of repeated experiments, which often leads to the damage of edges in the latent image and inaccurate blur kernel. The proposed blind deblurring model based on edge-preserving of L₀-regularized gradient (EP-L₀RG) prior has the great adaptability to the parameters selection for retaining the edges. The experimental results state that the proposed method not only reduces the blindness and difficulty of the parameter settings, but also estimates a more accurate kernel and improves the deblurring performance. Comparative experiments demonstrated that the proposed method provides the optimal and quantitative results.