Diode-pumped alkali lasers (DPALs) have drawn much attention since they were proposed in 2001. The narrow-linewidth DPAL can be potentially applied in the fields of coherent communication, laser radar, and atomic spectroscopy. In this study, we propose a novel protocol to narrow the width of one kind of DPAL, diode-pumped rubidium vapor laser (DPRVL), by use of an injection locking technique. A kinetic model is first set up for an injection-locked DPRVL with the end-pumped configuration. The laser tunable duration is also analyzed for a continuous wave (CW) injection-locked DPRVL system. Then, the influences of the pump power, power of a master laser, and reflectance of an output coupler on the output performance are theoretically analyzed. The study should be useful for design of a narrow-linewidth DPAL with the relatively high output.