Unlike a traditional fiber laser with a defined resonant cavity, a random fiber laser (RFL), whose operation is based on distributed feedback and gain via Rayleigh scattering (RS) and stimulated Raman scattering in a long passive fiber, has fundamental scientific challenges in pulsing operation for its remarkable cavity-free feature. For the time being, stable pulsed RFL utilizing a passive method has not been reported. Here, we propose and experimentally realize the passive spatiotemporal gain-modulation-induced stable pulsing operation of counterpumped RFL. Thanks to the good temporal stability of an employed pumping amplified spontaneous emission source and the superiority of this pulse generation scheme, a stable and regular pulse train can be obtained. Furthermore, the pump hysteresis and bistability phenomena with the generation of high-order Stokes light is presented, and the dynamics of pulsing operation is discussed after the theoretical investigation of the counterpumped RFL. This work extends our comprehension of temporal property of RFL and paves an effective novel avenue for the exploration of pulsed RFL with structural simplicity, low cost, and stable output.