In this paper, motivated by approximating the Euler-Lagrange equation of the pth-order regularization for 0 < p ≤ 1, we propose a new regularization model with adaptive diffusivity for variational image denoising. The model is equipped with a regularization controller which is introduced to adaptively adjust the diffusivity from pixel to pixel according to the magnitude of image gradient. The associated energy functional is convex and thus the minimization problem can be efficiently solved using a modified split Bregman iterative scheme. A convergence analysis of the iterative scheme is established. Numerical experiments are performed to demonstrate the good performance of the proposed model. Comparisons with some other image denoising models are also made.