We systematically study the cylinder-forming ABC triblock terpolymer thin films using canonical ensemble Monte Carlo simulations. The simulated annealing procedure is applied to the self-assembling process. By judicious choice of the system dimensions, we elaborately investigate the effect of film thickness on the orientation of the cylinders. This confined triblock terpolymer system exhibits different phase behavior under the weak and strong surface fields. In addition, we also investigate the ensemble-averaged chain orientations and relative density profiles.