We report a novel gain enhancement scheme for fiber-optic parametric amplifiers utilizing cascaded amplification and quasi-phase matching (QPM), The theory and method of QPM for four-wave mixing (FWM) are developed for the first time to our knowledge. In experimental implementations of the theory, we achieve >12 dB gain improvement in a three-stage dispersion-shifted (DS) fiber parametric amplifier. A 16-dB overall gain is obtained with 11 nm separation between zero-dispersion wavelength and pump wavelength. The experimental results show good agreement with theory and simulations. The influence of QPM on spectral characteristics of parametric gain is investigated with numerical simulations.