Recently, two-dimensional materials have attracted enormous attentions for electronic and optoelectronic applications owing to their unique surface structures and excellent physicochemical properties. Herein, the structural, electronic and optical properties of a series of novel monolayer InGeX3 (X = S, Se, Te) materials are investigated systematically by means of comprehensive first-principles calculations. All these three materials exhibit hexagonal symmetries and dynamical stabilities with no imaginary phonon mode. For monolayer InGeX3 (X = S, Se, Te), there exist obvious In-X ionic bonds and the partially covalent interactions of Ge-Ge and Ge-X. By using the HSE06 method, the band gaps of monolayer InGeX3 are predicted to 2.61, 2.24 and 1.80 eV, respectively. Meanwhile, the p-s orbital hybridizations are happened between X and In atoms in the conduction band regions and their interactions become smaller with the increase of X atomic number. In addition, the dielectric function, absorption coefficient and reflectivity spectra of monolayer InGeS3, InGeSe3 and InGeTe3 show the strong optical peaks along the in-plane direction in the UV light region. The definite bandgaps and optical properties make monolayer InGeX3 (X = S, Se, Te) materials viable candidates for future electronic and optoelectronic applications.