Nano-gas bubble superlattices are often observed in irradiated UMo nuclear fuels. However, the formation mechanism of gas bubble superlattices is not well understood. A number of physical processes may affect the gas bubble nucleation and growth; hence, the morphology of gas bubble microstructures including size and spatial distributions. In this work, a phase-field model integrating a first-passage Monte Carlo method to investigate the formation mechanism of gas bubble superlattices was developed. Six physical processes are taken into account in the model: 1) heterogeneous generation of gas atoms, vacancies, and interstitials informed from atomistic simulations; 2) one-dimensional (1-D) migration of interstitials; 3) irradiation-induced dissolution of gas atoms; 4) recombination between vacancies and interstitials; 5) elastic interaction; and 6) heterogeneous nucleation of gas bubbles. We found that the elastic interaction doesn't cause the gas bubble alignment, and fast 1-D migration of interstitials along <110> directions in the body-centered cubic U matrix causes the gas bubble alignment along <110> directions. It implies that 1-D interstitial migration along [110] direction should be the primary mechanism of an fcc gas bubble superlattice which is observed in bcc UMo alloys. Simulations also show that fission rates, saturated gas concentration, and elastic interaction all affect the morphology of gas bubble microstructures.