Detailed analyses of the short-term stability of the semiconductor fiber ring laser (SFRL) are presented. Analysis with rate equations shows that the relaxation oscillation effect does not exist in the SFRL. With a frequency-domain model, the mode competition in the SFRL is shown to be suppressed by the gain saturation effect of the semiconductor optical amplifier. Thus the observed good short-term stability of SFRL is theoretically explained. The analyses are verified in experiments.