The growth of homoepitaxial GaN, AlGaN layers, and GaN/AlGaN multiple quantum wells (MQWs) on Ga- and N-faces of bulk GaN single crystal substrates prepared by pressure-controlled solution growth (PC-SG) has been performed by radio-frequency molecular-beam epitaxy (RF-MBE). It was determined that homoepitaxial GaN layers grown on both Ga- and N-faces had good crystallinity with narrow full-width at half maximum (FWHM) of 150 and 94 arcsec for the (0002) plane and 119 and 106 arcsec for the (10-12) plane in x-ray rocking curve measurements, respectively. Crack-free AlGaN epilayers with Al mole fraction up to 30% were obtained on both faces. AlGaN epilayers on Ga-faces with higher Al mole fraction than those on N-faces under the same Al flux condition were obtained. Furthermore, phase separation existed only in the AlGaN epilayers grown on N-faces. The 5 K photoluminescence spectra for the GaN/AlGaN MQW structures grown on Ga-faces at peak energy of 3.419 to 3.686 eV can be obtained by varying the well thickness from 18 to 2 ML.