Passively mode-locked fiber laser (MLFL) has been widely used in many applications, such as optical communication system, industrial production, information processing, laser weapons and medical equipment. And many efforts have been done for obtaining lasers with small size, simple structure and shorter pulses. In recent years, nonlinear polarization rotation (NPR) in semiconductor optical amplifier (SOA) has been studied and applied as a mode-locking mechanism. This kind of passively MLFL has faster operating speed and makes it easier to realize all-optical integration. In this paper, we had a thorough analysis of NPR effect in SOA. And we explained the principle of mode-locking by SOA and set up a numerical model for this mode-locking process. Besides we conducted a Matlab simulation of the mode-locking mechanism. We also analyzed results under different working conditions and several features of this mode-locking process are presented. Our simulation shows that: Firstly, initial pulse with the peak power exceeding certain threshold may be amplified and compressed, and stable mode-locking may be established. After about 25 round-trips, stable mode-locked pulse can be obtained which has peak power of 850mW and pulse-width of 780fs.Secondly, when the initial pulse-width is greater, narrowing process of pulse is sharper and it needs more round-trips to be stable. Lastly, the bias currents of SOA affect obviously the shape of mode-locked pulse and the mode-locked pulse with high peak power and narrow width can be obtained through adjusting reasonably the bias currents of SOA.