Strong photoluminescence was observed from nominally pure lanthanum aluminate crystals and related materials with perovskite structure in a visible and ultraviolet wavelength regions. Single crystals of RAlO3 (R equals La, Y, Nd, Sm) were grown with a floating-zone method in reduced atmosphere. Photoluminescence from as-grown LaAlO3 single crystals was composed of a fast ultraviolet component and a broad visible emission. From the lifetime measurement, absorption spectra, excitation spectrum, and comparison between samples as-grown and annealed in oxygen, we assigned the visible component to the emission from excited state formed at oxygen defect sites because the emission was strongly suppressed with oxidation. On the other hand, the UV emission was assigned to band-to-band emission or emission from polaron pairs. Similar two components were observed in YAlO3 crystals at longer wavelength region than in LaAlO3. Fast UV emission was observed also in NdAlO3 and SmAlO3. Because it is possible to make some perovskite crystals electrically conductive by varying the concentration of dopants, the combination of luminescence and electrical conductivity in perovskite oxides make them auspicious materials for novel optoelectronic devices. Our results show the possibility of light-emitting devices made of perovskite aluminate crystals.