Measurements by Belle Collaboration of the cross section for inclusive J/y production in e(c)(+e- annihilation have been a serious challenge to current heavy-quarkonium theory. In particular, the measured cross sections for exclusive J/y+h) and inclusive J/y+c (c) over bar +X differ from nonrelativistic QCD predictions by an order of magnitude. In order to check if other available alternative theories can resolve such a large discrepancy, we calculate the cross section for inclusive J/y+c (c) over bar +X based on the color-evaporation model. As a phenomenological model, the color-evaporation model is still employed to predict cross sections for inclusive quarkonium production in various processes. Our results show that the color-evaporation-model prediction is even smaller than the nonrelativistic QCD prediction by an order of magnitude. The resultant color-evaporation-model prediction for the J/y+c (c) over bar +X fraction in the inclusive J/y production cross section is 0.049, while the empirical value measured by Belle Collaboration is 0.82.