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In this paper, we study the dynamic characteristics of fractional-order nonlinear financial systems, including bifurcation and local asymptotic stability. Among them, we select the elasticity of demand of commercial (EDC) as the bifurcation point to discuss the state of the system. By calculating, the lowest order bifurcation point is obtained. Furthermore, the impulse control gains that follow a fractional-order control law are applied to make the fractional-order nonlinear financial system stable. In addition, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed state form of the system near the bifurcation point and the states of the system when the impulse control is used or not.