Based on Newton-Raphson method for nonlinear system of equations,a shooting algorithm for mathematic model of backward multi-pumped Raman fiber amplifier(BMP-RFA) is presented.The simulations for the BMP-RFA under various practical parameters showed that the shooting algorithm is stable and efficient.For the BMP-RFA case proposed by ITU,in which 100 channels spaced by 100 GHz in the C+L band between 1 530.33 nm and 1 611.79 nm are pumped at 1 420 nm,1 440 nm,1 460 nm,1 480 nm and 1 500 nm simultaneously,the simulation reached a 0.3 mW maximum power deviation from the target pump power after 4 iterations.The power for each signal channel is 1 mW,the target power of each pump is 220 mW,and the gain medium is a 20 km long standard single mode fiber.