For the problem that the existing grey models are not applicable to forecast small sample oscillating sequences, a grey forecasting method for these sequences based on Fourier series is proposed. Firstly, a GM(1,1) power model of the original sequence is built to describe the behavior of the system overall trend. Then, Fourier series is used to extract of the periodic oscillation law contained in the residual sequence, thus a new time response function is formed by adding the two parts. Finally, the average error is minimized as the goal to establish the nonlinear optimization model for solving the optimal parameters. Numerical simulation and application examples show that simulation and forecasting accuracy are effectively enhanced.