Based on Jones matrices, a numerical model is proposed for the simulation of nonlinear polarization rotation (NPR) mode-locked fiber lasers with the advantage of a clear physical meaning. Ultra short pulses are derived with symmetric shape, stable amplitude and a square width of 0.28 ps. A self-starting NPR mode-locked fiber laser experimental setup is established and the fundamental repetition of the pulses is 67.35 MHz. Both the numerical simulation and the experimental results indicate that the angle of the half wave plate has a period of 180 while the quarter wave plate has a period of 90. Due to the influence of random birefringence, the tuning range of the angle of the wave plates measured in experiment is smaller than that shown in numerical simulation, which is verified by adding the effect of random birefringence in numerical simulation.