Single sensor digital cameras use CFA to sample red, green and blue colors such that each sensor pixel only obtains one color sample. The interpolation process called CFA demosaicking can be utilized to reconstruct the full color image. In this paper, a new color filter array interpolation algorithm based on 2D discrete 3 \(\times \) 4 order HMM is proposed, which can capture the dependency among diagonal states. In order to obtain the desirable model parameters, the re-estimation formulas are derived using the EM algorithm and the Forward–Backward algorithm. The missing color samples are obtained after estimating the state of the missing pixels by the 2D Viterbi algorithm and the adaptive processing. The results of the experiment show that the proposed method has a better performance not only in the objective evaluations but also in the subjective visual measurement, compared with several state-of-the-art demosaicking methods.