To improve the lifetime and output power in a sealed-off $CO_2$ laser, a series of Nd$_{1-x}$Sr$_x$CoO$_3$(x = 0.0, 0.25, 0.40, 0.50, 0.60, 0.75) perovskite-type compounds has been synthesized and used for a cathode material. Using a typical method samples were sintered at 1150$^{circ}$C and their structures were determined as a cubic form by means of XRD analysis. The degrees of $CO_2$ dissociation were measured by PAS (photoacoustic spectroscopy) with the lapse of time. In the case of $Nd_{0.4}$Sr$_{0.6}$$CoO_3$, which showed the highest catalytic cathode effect, only 7% of the initial $CO_2$ concentration were dissociated at 30 torr of gas mixture and 5 mA of discharge current. The more the gas pressure decreased and the discharge current increased, the more the degree of dissociation occurred. The ability of catalytic cathode to regenerate CO$_2$ in the laser cavity lies in order for x, 0.60 > 0.50 > 0.40 > 0.75 > 0.25 ${gg}$ 0.0. Except for the case of x = 0.0 the amounts of $CO_2$ dissociation were found to be within 7-15% of the initial $CO_2$ concentration.