Total variation (TV) is well capable of preserving edges and smoothing flat regions, however, often suffers from staircase artifacts in regions with gradual intensity variations. The established second-order TV can overcome this drawback but may lead to blurred edges and boundaries in restored images. In current literature, their nonconvex extensions have been proven to be effective for further enhancing image quality. This paper proposes an edge-preserving image restoration model by using both nonconvex first- and second-order TV regularizers, with a box constraint. The nonconvex hybrid regularizer is able to significantly suppress the staircase artifacts while preserving the valuable edge information. The addition of the box constraint provides a visible positive effect on image restoration, especially when there are many pixels with values lying on the predefined dynamic range boundaries. In what follows, to guarantee solution efficiency and stability, we develop an iteratively reweighted algorithm based on alternating direction method of multipliers (ADMM) to solve the proposed constrained nonconvex hybrid variational model. Numerous experimental results have demonstrated the superior performance of our proposed method in terms of quantitative and qualitative image quality evaluations.