• Image restoration is a computationally intensive problem as a large number of pixel values have to be determined. • Since the pixel values of digital images can attain only a finite number of values. • In this paper, develop a new box-constrained multiplicative iterative (BCMI) algorithm for box-constrained image restoration. • The BCMI algorithm just requires pixel wise updates in each iteration, and there is no need to invert any matrices. • Then give the convergence proof of this algorithm and apply it to total variation image restoration problems, where the observed blurry images contain Poisson, Gaussian, or salt-and-pepper noises.