Oxygen reduction reaction (ORR) in a double perovskite material is considered to be the most sluggish reaction in the intermediate temperature operation of a solid oxide fuel cell (SOFC). ORR is often inhibited by poor oxygen surface exchange rates or bulk diffusion in the material. In order to understand the rate-limiting process of the material, we have fabricated a dense thin-film double perovskite of composition Sr₂CoNbO_6-δ. The pulse laser deposition (PLD) method is employed to fabricate geometrically well-defined symmetric electrodes of SCN on an electrolyte substrate for accurate assessment of electrode impedance. Electrode thickness is varied from 40 nm to 80 nm by changing the deposition parameters in PLD. On increasing the thickness, the electrode impedance is observed to increase, suggesting bulk diffusion of oxygen anions limiting the electrochemical performance in the electrode material.