By the use of a set of coupled equations, the gain expression of two-pump fiber optical parametric amplifier (FOPA) with three-section nonlinear fibers is deduced theoretically. It is indicated that the parametric gain has a relationship with the pumps power, the fiber′s length and the fiber′s dispersion characteristic as well. From abnormal dispersion region to normal dispersion region, the bandwidth reduced and became flattened. Assume the fiber′s second-order dispersion keeps constant, with the increase of the fiber′s fourth-order dispersion, the bandwidth is reduced accordingly. By using multi-section fiber arrangement, the parametric gain can be flattened by adjusting the fiber′s parameters.