The indirect bandgap of two-dimensional GaN hinders its application in the optical field. Hydrogenation can convert the bandgap type of the GaN monolayer from an indirect to a direct one and also tune the bandgap size. The thermal transport, an important property in the application of two-dimensional materials, is also influenced by hydrogenation. By performing first-principles calculations and solving the phonon Boltzmann equation, we investigate the effect of hydrogenation on the thermal conductivity of the GaN monolayer. The results show that hydrogenation will slightly increase the thermal conductivity of the GaN monolayer from 70.62 Wm-1 K-1 to 76.23 Wm-1 K-1 at 300 K. The little effect of hydrogenation on thermal conductivity is mainly dominated by two competing factors: (1) the reduction of ZA mode lifetime due to the breaking of reflection symmetry after hydrogenation and (2) the increased contribution from TA and LA modes due to the reduction of anharmonic scattering caused by the enlarged phonon bandgap after hydrogenation. The results are compared with other two-dimensional materials with hexagonal monolayer structures.