A novel approach based on long short-term memory (LSTM) networks that can incorporate multivariate time series data, including historical tourism volume data, search engine data and weather data, is proposed for forecasting the daily tourism volume of tourist attractions. The proposed approach is applied to forecast the daily tourism volume of Jiuzhaigou and Huangshan Mountain Area, two famous tourist attractions in China. Through these two applications, the validity of the proposed approach is verified. In addition, the forecasting power of the approach with historical data, search engine data and weather data is stronger than that without search engine data or without both search engine data and weather data, which provides evidence that search engine data and weather data are of great significance to tourism volume forecasting. •A forecasting approach with long short-term memory networks is proposed.•Historical data, search engine data and weather data are all used in modelling.•The forecasting approach can automatically learn the time lags of observations.•Daily tourism volume for two tourist attractions is forecasted with the new approach.•Search engine data and weather data are of great significance for forecasting.