The problem we will consider in this paper is binary image restoration. It is, in essence, difficult to solve because of the combinatorial nature of the problem. To overcome this difficulty, we propose a new minimization model by making use of a new variable to enforce the image to be binary. Based on the proposed minimization model, we present a fast alternating minimization algorithm for binary image restoration. We prove the convergence of the proposed alternating minimization algorithm. Experimental results show that the proposed method is feasible and effective for binary image restoration.