The thiospinel CuIr2S4 exhibits a temperature-induced metal-insulator (M-I) transition around 226 K, showing hysteresis on heating and cooling, that manifests itself as a gap in the electronic density of state with increasing electrical resistivity at low temperatures. Conversely, CuIr2Se4 remains metallic down to 0.5 K. We have successfully synthesized the spinel-type compound CuIr2(S1-xSex)4 system. In order to see the effect of substitutions of Se at the S sites, we have carried out a systematic experimental study of structural, electrical, and magnetic properties of CuIr2(S1-xSex)4. Mössbauer spectroscopy measurements of 193Ir have been performed for CuIr2S4 and CuIr2Se4. The M-I transition of CuIr2(S1-xSex)4 for x<~0.15 is accompanied by a structural transformation from tetragonal (low-temperature insulating phase) to cubic (high-temperature metallic phase) symmetry. With increasing Se concentration x, the sharp M-I transition shifts to lower temperature. The resistivity shows a monotonous increase with decreasing temperature for 0.17<~x<~0.78 between 4.2 and 300 K, and the metallic state is recovered for x>~0.80. Magnetic susceptibility measurements show the jump at the M-I transition temperature with hysteresis on heating and cooling. The high-temperature metallic phase of CuIr2S4 shows Pauli paramagnetism, having a density of states at the Fermi level, D(εF)=0.67 states/eV atom. The insulating phase at low temperatures exhibits diamagnetism, and there is no localized magnetic moment. The Arrhenius regime is observed for the conductivity with a thermally activated process for 0<~x<~0.70 in the insulating phase. There is a general trend toward increasing metallicity with increasing x, which is consistent with the magnetic susceptibility results. A possibility of a two-site model of different valence states for Ir ions in the insulating phase of CuIr2S4 will be discussed on the basis of the Mössbauer data. A phase diagram of temperature versus Se concentration x will be proposed for the CuIr2(S1-xSex)4 system. The mechanism of the M-I transition remains enigmatic and is far from a complete picture.