Fire plays a significant role in global atmosphere and biosphere carbon and nutrient cycles. Globally, there are substantially different distributions and impacts between fire occurrence and fire intensity. It is prominent to have a thorough investigation of global relationship between fire occurrence and fire intensity for future fire prediction and management. In this study, we proposed an intermediate fire occurrence-intensity (IFOI) hypothesis for the global relationship between fire occurrence and fire intensity, suggesting that fire occurrence changes with fire intensity following a humped relationship. We examined this hypothesis via satellite data from January 2001 to December 2013 at a global scale, and in small and large fire intensity zones, respectively. Furthermore, the fire occurrence and fire intensity relationship was developed among different vegetation types to reveal the changes of parameters and strengths. Finally, the environmental factors (including climatic, hydraulic, biological, and anthropogenic variables) underpinning the fire occurrence and intensity pattern were evaluated for the underlying mechanisms. The results supported our IFOI hypothesis and demonstrated that the humped relationship is driven by different causes among vegetation types. Fire occurrence increases with fire intensity in small fire intensity zones due to alleviation of the factors limiting both fire occurrence and intensity. Beyond a certain fire intensity threshold, fire occurrence is constrained, probably due to the limitation of available fuels. The information generated in this study could be helpful for understanding global variation of fire occurrence and fire intensity due to fire-vegetation-climate-human interactions and facilitating future fire management.