The famous demonstration of optical rogue waves (RWs), a powerful tool to reveal the fundamental physics in different laser scenarios, opened a flourishing time for temporal statistics. Random fiber laser (RFL) has likewise attracted wide attention due to its great potential in multidisciplinary demonstrations and promising applications. However, owing to the distinctive cavity-free structure, it is a scientific challenge to achieve temporal localized RWs in RFLs, whose feedback arises from multiple scattering in disordered medium. Here, we report the exploration of RW in the highly skewed, transient intensity of an incoherently pumped RFL for the first time, to our knowledge, and unfold the involved kinetics successfully. The corresponding frequency domain measurements demonstrate that the RW event arises from a crucial sustained stimulated Brillouin scattering process with intrinsic stochastic nature. This investigation highlights a novel path to fully understanding the complex physics, such as photon propagation and localization, in disordered media.