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This work concerns the boundary integrability of the${\cal{U}}_{q}[osp(1|2)]$ Temperley-Lieb model. We constructed the solutions ofthe graded reflection equations in order to determine the boundary terms of thecorrespondig spin-1 Hamiltonian. We obtain the eigenvalue expressions as wellas its associated Bethe ansatz equations by means of the coordinate Betheansatz. These equations provide the complete description of the spectrum of themodel with diagonal integrable boundaries.

On the ${\cal{U}}_{q}[osp(1|2)]$ Temperley-Lieb model