The use of lattice-matched (0.09%) hxagonal oxide substrate, ScAlMgO4, has considerably improved the quality of ZnO films grown by laser molecular-beam epitaxy. Surface morphology was extremely smooth as represented by atomically Bat terraces and 0.26 nm high steps corresponding to the charge neutral unit of ZnO. Crystallinity was comparable to that of bulk single crystals: full-width at half-maximum value of ZnO(0 0 0 2) rocking curve was 39 arcsec. Optical absorption spectra showed clear splitting of A- and B-exciton lines, indicating low damping. Residual carrier concentration in pristine films was as low as 10(15) cm(-3) with keeping high electron mobility of similar to 100 cm(2)/Vs. Therefore, the ZnO films grown on ScAlMgO4(0001) substrates can be a starting point for realizing p-type ZnO. In fact, high concentration (similar to 10(21) cm(-3)) nitrogen can be doped with keeping high crystallinity.