The box constraints in image restoration have been arousing great attention, since the pixels of a digital image can attain only a finite number of values in a given dynamic range. This paper studies the box-constrained total-variation (TV) image restoration problem with automatic regularization parameter estimation. By adopting the variable splitting technique and introducing some auxiliary variables, the box-constrained TV minimization problem is decomposed into a sequence of subproblems which are easier to solve. Then the altating direction method (ADM) is adopted to solve the related subproblems. By means of Morozov0s discrepancy principle, the regularization parameter can be updated adaptively in a closed form in each iteration. Image restoration experiments indicate that with our strategies, more accurate solutions are achieved, especially for image with high percentage of pixel values lying on the boundary of the given dynamic range.