Narrow-linewidth nanosecond pulsed Raman fiber amplifiers possess many applications such as in nonlinear frequency generation, remote sensing and quantum information. By considering nonlinear effects such as stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), self-phase modulation (SPM) and cross-phase modulation (XPM), we build a nonlinear dynamical model of narrow-linewidth nanosecond pulsed Raman fiber amplifier. A numerical simulation model is also built and the simulation is carried out based on the parallelizable bidirectional finite difference time-domain method. The pulse evolution processes in time and spectral domain are simulated. The influences of pump pulse width, fiber length and signal laser power are studied in detail. It is found that SRS peak power threshold is not influenced by pump pulse width, however, pump pulse width will affect SBS threshold and output linewidth. When the pump pulse width is 800 ns, tens of MHz narrow linewidth can be obtained, but the SBS occurs as the increasing of pump energy, which limits the power scaling of the narrow-linewidth laser pulses. When the pump pulse width is 80 ns, the SBS is effectively suppressed and the peak power can be further increased, but the linewidth of output laser is easily broadened to hundreds of MHz. The simulation results also show that lower SRS threshold and higher efficiency can be obtained by using longer passive fiber, however, if shorter passive fiber is used, SPM and XPM can be weakened and narrower linewidth can be obtained. We build an experimental setup to study the influence of fiber length. In our experiment, a polarization-maintained passive fiber with a core diameter of 10 m and core numerical aperture of 0.08 is used as the Raman gain fiber. The signal laser is a 1120 nm single frequency continuous wave fiber laser with an average power of 20 mW, and the pump laser is a 1064 nm pulsed laser with a pulse width of~40 ns and repetition rate of 500 kHz. When the fiber lengths are 100 m and 80 m, the efficiencies of the pulsed Raman amplifier are, respectively, 51.5% and 38.2% at a pump power of 6.8 W. It can also be found that increasing signal power can increase the efficiency of the amplifier, but it will reduce the SBS threshold at the same time. Therefore, in order to balance the different nonlinear effects in the arrow-linewidth nanosecond pulsed Raman fiber amplifier, we should take laser power, linewidth and efficiency into consideration, and choose the suitable system parameters such as pump pulse width, fiber length and signal power. These analyses can serve as design guidelines for narrow-linewidth nanosecond pulsed fiber Raman amplifiers.