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This paper performs first-principles calculations to study the structural, mechanical and electronic properties of the spinels ZnAl2O4, ZnGa2O4 and ZnCr2O4, using density functional theory with the plane-wave pseudopotential method. Our calculations are in good agreement with previous theoretical calculations and the available experimental data. The studies in this paper focus on the evolution of the mechanical properties of ZnAl2O4, ZnGa2O4 and ZnCr2O4 under hydrostatic pressure. The results show that the cubic phases of ZnAl2O4, ZnGa2O4 and ZnCr2O4 become unstable at about 50 GPa, 40 GPa and 25 GPa, respectively. From analysis of the band structure of the three compounds at equilibrium volume, it obtains a direct band gap of 4.35 eV for ZnAl2O4 and 0.89 eV for ZnCr2O4, while ZnGa2O4 has an indirect band gap of 2.73 eV. [ABSTRACT FROM AUTHOR]