Cascaded fiber optical parametric amplifier (FOPA) can enhance gain and bandwidth. The gain and bandwidth can be further enhanced by dithering the FOPA pump. However, to our knowledge, the effects of a pump dithering at every stage of cascaded FOPA have not been discussed. The study of performance at every stage of cascaded FOPA is quite interesting and beneficial in designing the system. Here, we analyzed, using OptiSystem software, each stage of a cascaded FOPA, when there was a pump dithering and not. The results showed that the pump dithering enhanced the gain and broaden the bandwidth at every stage. The gain and bandwidth obtained with the pump dithering were 27 dB and 20 nm, respectively. On the other hand, when there was no pump dithering, the gain and bandwidth were 9 dB and 12 nm, respectively.