Diode-pumped alkali lasers (DPALs) have undergone rapid development to become one of the most promising candidates for use as high-power laser sources in recent years. Relaxation oscillation (RO) is a common phenomenon related to the dynamic process in the time domain. Sometimes, it is applied in parameter measurement, but sometimes it should be eliminated to ensure stable output. In this paper, we develop a kinetic model to study the RO features of a DPAL, which are different from those of a conventional solid-state laser. The results reveal that the cell temperature, buffer gas pressure, pumping power, cavity length, and reflectance of an output coupler affect the characteristics of ROs. Among these parameters, the cell temperature and the pumping power exert relatively strong influences on the waiting time of the first spike in the RO. Additionally, the cavity length cannot markedly affect the peak value of the laser intensity. These new analyses should prove useful for understanding the dynamic process of DPAL oscillation and for the future design of a steady high-powered DPAL.