Considering phase compensation and small signal condition, we derive the four-wave-mixing coupling equations of the cascaded fiber optical parametric amplifier (CFOPA), from which the expressions of the output gain and phase are obtained. Utilizing the obtained expressions, the gain and bandwidth characteristics of CFOPA are analyzed and further compared with the single-segment fiber optical parametric amplifier(SFOPA). The 3 dB bandwidth of the CFOPA can reach 67.2 nm when the dispersion-shifted fiber (DSF) is dividing into ten segments, but the SFOPA is just 12.6 nm. So the bandwidth is increased 54.6 nm through cascading compensation. And then, the 3 dB bandwidth of the CFOPA will remain the same, but the gain decreases when considering the fiber loss and splice loss. Results show that the bandwidth can be broadened significantly by introducing multi-segments cascading compensation to DSF, and the obtained bandwidth is observed much broader and flatter when compared with that of SFOPA for a given DSF length, pumping power, or idle power.