AlGaN/GaN heterostructures with multiple quantum wells were grown by plasmaassisted molecular beam epitaxy (PAMBE). Structural and optical properties of the heterostructures were analyzed using x-ray diffraction, cathodoldminescence, and photoluminescence. Interband transitions were clearly observed in the GaN quantum wells at both room- and liquid-helium temperatures. The efficiency of the interband recombination due to the confinement effect was greatly enhanced in the thinner quantum wells. The functional dependence of the interband peaks on the well thickness is shown to be in good agreement with the calculated positions of the quantized levels in the wells.