Accurate estimation of the gross primary production (GPP) of terrestrial vegetation is vital for understanding the global carbon cycle and predicting future climate change. Multiple GPP products are currently available based on different methods, but their performances vary substantially when validated against GPP estimates from eddy covariance data. This paper provides a new GPP dataset at moderate spatial (500 m) and temporal (8-day) resolutions over the entire globe for 2000-2016. This GPP dataset is based on an improved light use efficiency theory and is driven by satellite data from MODIS and climate data from NCEP Reanalysis II. It also employs a state-of-the-art vegetation index (VI) gap-filling and smoothing algorithm and a separate treatment for C3/C4 photosynthesis pathways. All these improvements aim to solve several critical problems existing in current GPP products. With a satisfactory performance when validated against in situ GPP estimates, this dataset offers an alternative GPP estimate for regional to global carbon cycle studies.