Based on the first-principles calculations, we identify four stacking patterns of the GeS bilayer, in which two most stable ones are almost equally stable. The most stable one corresponds to the experimental pattern in bulk GeS. Its interlayer binding is stronger than those in a-phosphorene and graphene, indicating that the material will rather exist in the form of bilayers or multilayers. Our HSE06 band structure calculations show that both patterns are semiconductors with indirect band gaps in the visible region, which are slightly smaller than that of the monolayer. For the monolayer, our refined calculation based on the deformation potential approximation indicates that the electron mobility along the armchair direction amounts to 4.62×10 4 cm 2 V -1 s -1 , which is ~40 times larger than that of the a-phosphorene. The electron mobility of the bilayer is dependent on the stacking pattern. The most stable pattern is expected to exhibit the mobility of 1.69×10 4 cm 2 V -1 s -1 , which is still ~30 times larger than that of the bilayer a-phosphorene. A detailed comparison of the carrier mobilities suggests that both of the mono- and bi-layer will be useful for n-type electronics.