Spatiotemporal patterns of global forest net primary productivity (NPP) are pivotal for us to understand the interaction between the climate and the terrestrial carbon cycle. In this study, we use Google Earth Engine (GEE), which is a powerful cloud platform, to study the dynamics of the global forest NPP with remote sensing and climate datasets. In contrast with traditional analyses that divide forest areas according to geographical location or climate types to retrieve general conclusions, we categorize forest regions based on their NPP levels. Nine categories of forests are obtained with the self-organizing map (SOM) method, and eight relative factors are considered in the analysis. We found that although forests can achieve higher NPP with taller, denser and more broad-leaved trees, the influence of the climate is stronger on the NPP; for the high-NPP categories, precipitation shows a weak or negative correlation with vegetation greenness, while lacking water may correspond to decrease in productivity for low-NPP categories. The low-NPP categories responded mainly to the La Niña event with an increase in the NPP, while the NPP of the high-NPP categories increased at the onset of the El Niño event and decreased soon afterwards when the warm phase of the El Niño-Southern Oscillation (ENSO) wore off. The influence of the ENSO changes correspondingly with different NPP levels, which infers that the pattern of climate oscillation and forest growth conditions have some degree of synchronization. These findings may facilitate the understanding of global forest NPP variation from a different perspective.