The catalytic activity of $Nd_{1-x}Sr_xCoO_{3-y}$, $0{leq}x{leq}0.75$ and $0.001{leq}y{leq}0.103$, on the oxidation of carbon monoxide has been investigated from the structure analyses of the catalysts by X-ray diffraction and infrared spectroscopy and the measurements of the oxidation and adsorption rates of carbon monoxide. The catalytic activity is found to be correlated with Sr substitution (x) and nonstoichiometry (y). The oxidation power of carbon monoxide increases continuously with increasing Sr substitution without oxygen, but increases with Sr substitution up to x = 0.25 and then is almost constant at larger x values up to x = 0.75 with oxygen. This change of catalytic activity is explained by the oxidation-reduction properties of the catalyst due to the variation of nonstoichiometry.