The traditional algorithm cannot get rid of the influence of correlated noise on underwater images. In view of this, this paper proposes a restoration algorithm to restrain the correlated noises of underwater images by establishing a variational model based on the theory of maximum a posteriori estimation that represents convex property. In the variational model, the probability distribution of noise is guaranteed via the item of Bayesian restraint. Meanwhile the property of spatial continuity is satisfied via the Markov constraint. The gradient method is employed to obtain the optimal solution of the variational model, i.e. the restoration image without correlated noise. Experimental results show the correlated noise is eliminated by the proposed algorithm effectively; the restoration images present an excellent visual effect. ©, 2015, Editorial Board of Journal of HEU. All right reserved.