In this paper, a simplified 2-D second-order Hidden Markov Model (HMM) with tied state mixtures is applied to the face recognition problem. The mixture of the model states is fully-tied across all models for lower complexity. Tying HMM parameters is a well-known solution for the problem of insufficient training data leading to non-robust estimation. We show that parameter tying in HMM also enhances the resolution in the case of small model. The performance of the proposed 2-D HMM tied-mixture system is studied for the face recognition problem and the expected improved robustness is confirmed.