The 2009 influenza pandemic teaches us how fast the influenza virus could spread globally within a short period of time. To address the challenge of timely global influenza surveillance, this paper presents a spatial-temporal method that incorporates heterogeneous data collected from the Internet to detect influenza epidemics in real time. Specifically, the influenza morbidity data, the influenza-related Google query data and news data, and the international air transportation data are integrated in a multivariate hidden Markov model, which is designed to describe the intrinsic temporal-geographical correlation of influenza transmission for surveillance purpose. Respective models are built for 106 countries and regions in the world. Despite that the WHO morbidity data are not always available for most countries, the proposed method achieves 90.26 to 97.10 percent accuracy on average for real-time detection of global influenza epidemics during the period from January 2005 to December 2015. Moreover, experiment shows that, the proposed method could even predict an influenza epidemic before it occurs with 89.20 percent accuracy on average. Timely international surveillance results may help the authorities to prevent and control the influenza disease at the early stage of a global influenza pandemic.