  The quantum $\tau_2$-model with generic site-dependent inhomogeneity and
arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method.
The eigenvalues of the corresponding transfer matrix are given in terms of an
inhomogeneous T-Q relation, which is based on the operator product identities
among the fused transfer matrices and the asymptotic behavior of the transfer
matrices. Moreover, the associated Bethe Ansatz equations are also obtained.
