We investigate the evolution of the molecular abundance in circumstellar disks around pre-main-sequence stars, taking into account the adsorption of molecules onto grains as well as the reactions in the gas phase. We follow the molecular evolution for some model disks, solving numerically the reaction equations. We show only the results on the abundance of CO molecules in the gas phase. There is a critical distance from the star, Rcrit, at which the temperature is equal to the critical temperature 20 K for the adsorption of CO molecules. At R > Rcrit, CO molecules are depleted rather rapidly from the gas phase mainly because of adsorption. Even in the region just inside Rcrit, CO molecules are depleted slowly because by gas-phase reactions, they are transformed into the other molecules that can be adsorbed more easily than CO. For the minimum-mass solar nebula extended to the region of radius R ≍ 800 AU, for example, CO molecules in the gas phase at R > Rcrit ≍ 200 AU are depleted by a few orders of magnitude in 105-106 yr, while at R <:Rcrit, the depletion of CO is not significant in these timescales. This is consistent with the recent observations of the gaseous disks around some T Tauri stars.