Optical properties in undoped ZnO thin films grown with laser-molecular beam epitaxy method on lattice-matched ScAlMgO4 substrates have been investigated. The transmission spectrum on this substrate at 6 K has two sharp peaks both of which are attributed to resonances of A- and B-excitons, which reflects small nonradiative damping constant of excitons as well as high film crystallinity accomplished by virtue of lattice matching. This is, to our best knowledge, the first observation of exciton absorption and its direct estimation of parameters related to A- and B-excitons.