We report on the optical properties of ZnO/(Mg, Zn)O multiple quantum wells (MQWs) on lattice-matched ScAlMgO4 substrates fabricated by laser molecular-beam epitaxy. As the well layer thickness decreased down to 7 Angstrom, the photoluminescence (PL) and absorption peaks showed a systematic blueshift, consistent with the quantum-size effect. Moreover, a bright PL of free excitons could be observed even at room temperature. As a result, the PL could be tuned in the energy range of 3.3-3.6 eV by choosing the appropriate barrier height and well layer thickness. The widest tunability on the room-temperature luminescence of the excitons could be attained on the basis of the ZnO quantum structure. These favorable properties could not be attained in the MQWs on lattice-mismatched sapphire substrates.