A governing equation of the six-wave fiber optical parametric amplifier (FOPA) for the power and phase difference evolution of the six interacting waves is deduced. To optimize the gain of the six-wave FOPA, a multivariate stochastic optimization algorithm, i.e., the genetic algorithm (GA), is applied. The effect of pump depletion on the gain characteristic of the six-wave FOPA is emphasized and the effect of the fiber length, the wavelength, and the power of two pumps on bandwidth, flatness, and magnitude of the gain spectrum has also been studied. A broader and flatter six-wave FOPA gain is obtained by adopting optimum design parameters, which theoretically provide a uniform gain of 65 dB with 0.3 dB uniformity over a 110 nm bandwidth for the six-wave FOPA.