The bandwidth of a single-pump fiber optical parametric amplifier is governed by the even orders of fiber dispersion at the pump wavelength. The amplifier can exhibit gain over a wide wavelength range when operated near the fiber's zero-dispersion wavelength. It can also be used for broadband wavelength conversion,with gain. We have experimentally obtained gain of 10-18 dB as the signal wavelength was tuned over a 35-nm bandwidth near 1560 nm.