To understand the behavior of electrons in a travelling-wave-type RF gun using the thermionic cathode with expectation of less backstreaming effects, gun electrode structures were studied to improve the electron beam properties for FELs. Electron trajectories in an RF gun were calculated by a 2-D simulation code newly developed with full Maxwell equations with space-charge effects taken into account self-consistently to evaluate RF gun performance characteristics, in particular, the effects due to backstreaming electrons and defocusing effects in the vicinity of the electrodes. Although several advantageous features are shown, the emittance for the TW RF gun is found inferior to the SW RF gun, due not to space-charge effects, but to defocusing electric fields in the vicinity of the disk aperture. Several methods for emittance improvements are proposed and shown successfully by numerical calculations.