Carbon monoxide (CO) is one of the best gas tracers in astrophysics including shocked gas. The shock wave can excite CO to very high excitation states, which are accessible to observations. In this work, we provide a post-processing scheme to model the line profile of the high-J CO rotational transitions from shocks with the Large Velocity Gradient (LVG) assumption. We use the shock properties computed by the Paris-Durham shock code, and demonstrate that the LVG assumption is applicable in the shocked gas. We numerically modeled a specific high-J CO line profile (rotational quantum number J = 15 → 14) and showed how its shape varies over the inclination angle. We found that the high−J CO transition can be treated as an optically thin line. The model can be extended to other CO transitions and molecules. This theoretical work is the first step in our project to study supernova remnant IC 443 using high−J CO data measured by GREAT instrument onboard SOFIA.