We　develop　a　Bayesian　estimation　method　to　non-parametric　mixed-effect　models　under　shape-constrains.　The　approach　uses　a　hierarchical　Bayesian　framework　and　characterizations　of　shape-constrained　Bernstein　polynomials　(BPs).　We　employ　Markov　chain　Monte　Carlo　methods　for　model　fitting,　using　a　truncated　normal　distribution　as　the　prior　for　the　coefficients　of　BPs　to　ensure　the　desired　shape　constraints.　The　small　sample　properties　of　the　Bayesian　shape-constrained　estimators　across　a　range　of　functions　are　provided　via　simulation　studies.　Two　real　data　analysis　are　given　to　illustrate　the　application　of　the　proposed　method.