We prove that the Grothendieck rings of category $\mathcal{ C}^{ (t)}_Q$ over quantum affine algebras $U_q'(\g^{ (t)})$ $(t=1,2)$ associated to each Dynkin quiver $Q$ of finite type $A_{ 2n-1}$ (resp. $D_{ n+1}$) is isomorphic to one of category $\mathcal{ C}_{ \mQ}$ over the Langlands dual $U_q'({ ^L}\g^{ (2)})$ of $U_q'(\g^{ (2)})$ associated to any twisted adapted class $[\mQ]$ of $A_{ 2n-1}$ (resp. $D_{ n+1}$). This results provide partial answers of conjectures of Frenkel-Hernandez on Langlands duality for finite-dimensional representation of quantum affine algebras.
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