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The effects of zero-dispersion wavelength (ZDWL) fluctuations on the noise characteristics of fiber optical parametric amplifiers (FOPAs) are investigated. The numerical derivation of the noise figure (NF) in terms of the amplifier operating conditions and the magnitude of ZDWL fluctuations is achieved by utilizing a simulation method based on the three-coupled propagation equations. The numerical analysis shows that the average NF of FOPAs is increased compared with the case of uniform dispersion, especially at high-gain operation. Apart from the NF, the gain-to-NF ratio is also evaluated to assess the amplifier performance for a variety of amplifier operating conditions and dispersion profiles.