Based on density functional theory and first-principles calculations, we systematically studied the structure, electronic and optical properties of bilayer MX2 (M = Ge, Sn and X = S, Se) materials. Our results show that the configuration of AB stacking is most stable among four kinds of MX2 (M = Ge, Sn and X = S, Se) stacking structures. The AB-stacked MX2 (M = Ge, Sn and X = S, Se) bilayers exhibit indirect band gaps ranging from 0.5 eV to 2.23 eV. It is found that the bilayer MX2 (M = Ge, Sn and X = 5, Se) configurations exhibit excellent optical absorption coefficient, especially in the deep ultraviolet region, which can reach 2 x 10(6) cm(-1). A high hole mobility along x direction is achieved in these specific stacking bilayers, which reaches an order of 10(3) cm(2) V-1 s(-1). Moreover, under biaxial strain and vertical electric field, the transition from semiconductor to metal occurs in bilayer GeS2 and bilayer SnS2, respectively.