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Purpose: Accurate foreign tourist arrivals forecasting can help public and private sectors to formulate scientific tourism planning and improve the allocation efficiency of tourism resources. This paper aims to address the problem of low prediction accuracy of Chinese inbound tourism demand caused by the lack of valid historical data. Design/methodology/approach: A novel hybrid Chinese inbound tourism demand forecasting model combining fractional non-homogenous discrete grey model and firefly algorithm is constructed. In the proposed model, all adjustable parameters of the fractional non-homogenous discrete grey model are optimized simultaneously by the firefly algorithm. Findings: The data sets of annual foreign tourist arrivals to China are used to verify the validity of the proposed model. Experimental results show that the proposed method is effective and can be used as a useful predictor for the prediction of Chinese inbound tourism demand. Originality/value: The method proposed in this paper is effective and can be used as a feasible approach for forecasting the development trend of Chinese inbound tourism. [ABSTRACT FROM AUTHOR]