Grey forecasting based on the grey system theory is a dynamic forecasting model and has been successfully applied in various fields. In recent years, many scholars have proposed new procedures or new models with different ways to improve the precision accuracy of grey forecasting for the fluctuating data sets. However, the prediction accuracy of the grey forecasting models existing may not be always satisfactory in different scenario. For example, the data not only including trend, seasonal as well as highly fluctuating are with lots of noise. To overcome this issue, this paper proposed two effective combined grey models named as Fourier Grey Model (1, 1) (abbreviated as F-GM (1, 1)) and Fourier Non Linear Grey Bernoulli Model (abbreviated as FRMGM (1, 1) are proposed in this paper. The proposed models were built by using Fourier series to modify their residual values. To verify the effectiveness of these proposed models, the international tourism demand in Vietnam from Jan 2005 to Feb 2015 is used for the modeling to forecast the international tourism demand from Mar 2015 to May 2015, and the forecasting results proved that the FRMGM (1, 1) is a better model in forecast the international tourism demand in Vietnam.