Due to triangular photonic crystal fiber (PCF) high nonlinearity and low dispersion slope, using the condition that the different linear phase shift combination must satisfy the phase match, the expressions of gain and bandwidth for one-pump fiber-optic parametric amplifiers (1P-FOPA) based on PCF in the normal and abnormal dispersion regimes are derived respectively. Then, 1P-FOPAs performance comparison among PCF, dispersion-shifted fiber (DSF) and highly nonlinear fibers (HNLF) are carried out by numerical simulations. It is shown that the 1P-FOPA based on triangular PCF can provide higher peak gain over wider bandwidth. When the pump wavelength is at the zero-dispersion wavelength (ZDWL), about 108.7 nm single-pass gain bandwidth and 91.4 dB peak gain can be obtained; when in the normal dispersion regime and near zero-dispersion wavelength, not less than 46 nm single-pass gain bandwidth 77.1 nm away from pump can be achieved. Finally the influence of dispersion fluctuation is analyzed, and the result shows that the tolerance of the 1P-FOPA based on photonic crystal fiber is better.fiber optical parametric amplifier, photonic crystal fiber, gain bandwidth, zero-dispersion wavelength variations