On basis of Herd-Scuseria-Emzerhof hybrid functional (HSE06) within the framework of density functional theory (DFT), we have computationally explored the intrinsic electronic and optical properties of two-dimensional (2D) methyl-terminated germanene (GeCH3). GeCH3 monolayer possesses an opportune direct band gap of 1.76 eV, which can be effectively tuned by applying elastic strain, and decreases with increasing the tensile strain while increases with small compressive strain. Also, anisotropic carrier mobility was disclosed in the armchair (x) and zigzag (y) direction of GeCH3 monolayer. Moreover, GeCH3 monolayer shows significant light absorption in the visible and ultraviolet range of solar spectrum, and is attractive for light harvesting. The results can help better understand the intrinsic properties of GeCH3 and provide reliable guidance for its experimental applications to electronics and optoelectronics.