Tourism demand plays a significant role in the formulation of tourism development policies by governments. While the GM(1,1) is the most frequently used grey prediction model, the Grey–Markov model has been applied to forecast tourism demand because it has advantages compared with the GM(1,1) model when the time series data fluctuate significantly. To further improve the predictive accuracy of the Grey–Markov model, two neural networks (NNs) are considered. One of the NNs is used to build an NNGM(1,1) such that the GM(1,1) does not need to determine the background value, and the other is used to estimate the degree to which a predicted value obtained from the NNGM(1,1) can be adjusted. We applied the proposed model to forecast the number of foreign tourists using historical annual data from Taiwan Tourism Bureau and China National Tourism Administration. The results showed that the proposed model outperforms other Grey–Markov models.