A two-dimensional mathematical model of carbon monoxide (CO) oxidation is investigated for the Langmuir-Hinshelwood mechanism on the surface of a Platinum (Pt) catalyst. The adsorbate-driven structural phase transition of catalytic surface is taken into account. The stability analysis of the model solutions is carried out. It is shown that the spatio-temporal periodic chemical oscillations of CO and oxygen (O) surface coverages and a fraction of the surface in the non-reconstructed (1 × 1)-structure occur. Conditions for Hopf and Turing bifurcation to arise are investigated.