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Based on the grey prediction model GM(1,1), a novel fractional-order grey prediction model is proposed and its modeling error is systematically studied. In this paper, exponential data sequences are generated for numerical simulation. Via the numerical simulation method, the mean absolute percentage error (MAPE) of the fractional-order GM(1,1) with different values of order and development coefficient is compared to the GM(1,1) and the discrete GM(1,1). The error distribution of the sequences of exponential data is given. The GM(1,1) and the direct modeling GM(1,1) are both special cases of the fractional-order GM(1,1). The conclusion is helpful to further optimize the grey model using fractional-order operators and to expand the applicable bound of GM(1,1).