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In this paper, neural network (NN) control of the fractional-order Duffing system (FODS) by using a backstepping method within finite time in the presence of input saturation has been investigated. A fractional-order filter with an order lying on the interval (1,2) was used to estimate the virtual input together with its fractional derivative, and this showed that the estimation error tends to a small region in some finite time. Fractional-order law is designed for the parameter of the NN, and an adaptive NN controller was given. The proposed method drives the tracking error, tending to an arbitrary small region within a finite time. The simulation results verify the validity of the proposed method.