Electronic structure and optical spectra of ZnX2O4 (X=Al, Ga, and In) have been studied by density functional calculations. It is shown that ZnX2O4 posses a large fundamental band gap and a second gap defined as the energy difference between the two lowest conduction band (CB) energies. The second gap is found to be similar to 2 eV for ZnAl2O4 and > 2.8 for ZnGa2O4 and ZnIn2O4. The bottommost CB for ZnX2O4 is well dispersive, which means that these materials possess the feature to conduct electrical current by CB electrons. Effective masses of electrons and holes are of the same order as those of the well-known ZnO and In2O3. Optimized equilibrium structural parameters and bulk modulus for ZnAl2O4 and ZnGa2O4 are found to be in good agreement with the available experimental values and these values for ZnIn2O4 are predicted. Chemical bonding is found to be mixed ionic-covalent with predominant ionic character.