Tourism demand forecasting has played an important role in supporting governments to devise development policies for travel and tourism. However, time series related to tourism often do not conform to statistical assumptions and feature significant temporal fluctuations. Because a Fourier series is often applied to oscillating sequences to remove noise, it is reasonable to develop a grey prediction model in conjunction with a Fourier series to forecast tourism demand. However, grey prediction models traditionally use one-order accumulation, treating each sample with equal weight, to identify regularities concealed in data sequences. Furthermore, when generating residuals from Fourier series, the prediction accuracy of the newly generated predicted values is not taken into account. In this study, by using fractional order accumulation to assign appropriate weights to samples, we propose a fractional grey prediction model with Fourier series that offers high prediction accuracy. Experimental results demonstrate that the proposed grey prediction model performs well compared with other considered prediction models.