  We study infinitely many commuting operators $T_B(z)$, which we call infinite
transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model. We diagonalize
infinite transfer matrix $T_B(z)$ by using free field realizations of the
vertex operators of the elliptic quantum group $U_{q,p}(A_{N-1}^{(1)})$.
