A femtosecond electron source has been developed at the Plasma and Beam Physics Research Facility (PBP), Chiang Mai University (CMU), Thailand. Ultra-short electron bunches can be produced with a bunch compression system consisting of a thermionic cathode RF-gun, an alpha-magnet as a magnetic bunch compressor, and a linear accelerator as a post acceleration section. To obtain effective bunch compression, it is crucial to provide a proper longitudinal phase-space distribution at the gun exit matched to the subsequent beam transport system. Via beam dynamics calculations and experiments, we investigate the bunch compression efficiency for various RF-gun fields. The particle distribution at the RF-gun exit will be tracked numerically through the alpha-magnet and beam transport. Details of the study and results leading to an optimum condition for our system will be presented.