Compton scattered radiation sources have been utilized in a broad range of experiments from fundamental science to industrial applications for their unique features, the generation of energy-tunable, nearly mono-energetic polarized photon beams. In the Compton radiation sources, the radiation bandwidth can be controlled by a collimator to restrict the scattering angle, but the bandwidth is also affected by the emittance and energy spread of the electron beam. In this study, we discuss collimator optimization to obtain narrow-band radiation from a Compton source with an electron beam having asymmetric emittance in the horizontal and vertical planes. A Monte Carlo simulation code based on Geant4 has been developed and used to compare circular and rectangular collimators for shaping the radiation spectrum of Compton sources.