Developing nanoelectronic engineering requires two-dimensional (2d) materials with both usable carrier mobility and proper large band-gap. In this study, we present a detailed theoretical investigation of the intrinsic carrier mobilities of buckled 2d GaN. This buckled 2d GaN is accessed by hydrofluorination (FGaNH) and hydrogenation (HGaNH). We predict that the anisotropic carrier mobilities of buckled 2d GaN can exceed those of 2d MoS2 and can be altered by an alterable surface chemical bond (convert from a Ga-F-Ga bond of FGaNH to a Ga-H bond of HGaNH). Moreover, converting FGaNH to HGaNH can significantly suppress hole mobility (even close to zero) and result in a transition from a p-type-like semiconductor (FGaNH) to an n-type-like semiconductor (HGaNH). These features make buckled 2d GaN a promising candidate for application in future conductivity-adjustable electronics.