We propose a MgAl2O4 substrate for GaN-based laser diodes. We grew GaN epitaxial layers using metal-organic vapor phase epitaxy on a MgAl2O4 substrate. The GaN on the MgAl2O4 showed a narrow X-ray diffraction peak of 310 arcsec, a photoluminescence dominated by the band-edge emission, and good electronic properties. The optical cavity was fabricated by cleaving the GaN on the MgAl2O4, and the stimulated emission from the cavity using optical pumping was observed. We also fabricated a light emitting diode (LED) with a AlGaN/InGaN double-heterostructure. The electroluminescence was dominated by the band-edge emission of InGaN with a narrow FWHM of 13.5 nm. The characteristics of LED on the MgAl2O4 were comparable to that on a A12O3 substrate. MgAl2O4 is feasible as a substrate for laser applications.