Inspired by the typical two-dimensional (2D) black-phosphorene-type structure with mm2 point-group symmetry, the structural stability, electronic structure, and intrinsic piezoelectricity of 2D ternary GaXY (X = Se and Te; Y = Cl, Br, and I) monolayers are systematically studied by the first-principles density functional theory. Our calculations show that these ternary monolayer compounds exhibit desirable dynamical and thermal stabilities and a large variety of bandgaps. The calculated piezoelectric coefficients d(11) is as large as 15.57 pm/V for GaTeF, and the largest d(12) reaches to 3.78 pm/V for GaSeI. It is worth noting that the e(ij) and d(ij) coefficients of GaXY monolayers display anisotropic periodic trends with respect to the constituent elements, which could be interpreted by a linear correlation between the piezoelectric coefficients and the differences in anionic polarizabilities alpha(X) or alpha(Y). It is found that d(11) of GaXY monolayers is directly proportional to (alpha(X) - alpha(Y)), while d(12) is inversely proportional to (alpha(X) - alpha(Y)). Such anisotropic correlation could be applicable to elucidate the origin of the piezoelectricity in other 2D ternary compounds. [GRAPHICS] .