Here, we present our numerical results of ZrxSi1-xO2 solid solutions (with x= 0-1) to predict new hypothetical tetragonal compounds of the Zircon family. We used the full potential linearized augmented plane wave (FP-LAPW) method based on DFT density functional theory in the GGA approximation as implemented in the WIEN2k code to study the structural and optoelectronic properties of the named compounds. First, we studied the properties of the compound ZrSiO4, where the obtained results are compared to several theoretical and experimental investigations. Secondly, we have predicted new hypothetical compounds for the ZrSi3O8 and Zr3SiO8 family that crystallize in the I41/amd space group. In any case, the chemical stability of the studied alloys has been verified with both the enthalpy of formation and the cohesive energy. Moreover, the phonon dispersion results also indicated this aspect. The electronic properties reveal a strong p-d covalent hybridization between Zr and O. The Zr3SiO8 compound exhibits a wide indirect band gap.