This article presents a non-stationary 1981–2012 AVHRR NDVI_3g time series. The AVHRR NDVI_3g dataset is an improved 8-km normalized difference vegetation index (NDVI) data set derived from AVHRR instruments, which have been flown or are flying on NOAA and EUMETSAT satellites. The dataset is composed of data from two AVHRR instruments: AVHRR/2 (1981–2000) and AVHRR/3 (2000–present). The main challenge in processing AVHRR NDVI data is to properly account for the limitations of the AVHRR instruments, including dual gain introduced in 2000 for AVHRR/3. To overcome these challenges, the authors used Bayesian methods with high-quality SeaWiFS NDVI data to derive AVHRR NDVI calibration parameters. The resulting NDVI values have an error of ±0.005 NDVI units, independent of time, and form a non-stationary climate dataset. The authors used Bayesian analysis to inter-calibrate AVHRR/2 and AVHRR/3 NDVI data, using SeaWiFS data to correct inconsistencies and produce a consistent non-stationary NDVI_3g dataset. The Bayesian approach allows for the estimation of probability distributions and the correction of biases in the AVHRR NDVI data. The resulting NDVI_3g dataset has high spatial and temporal coherence, with a low error of ±0.002 NDVI units. The dataset is used to study climate-related seasonal and inter-annual variability in vegetation. The authors conclude that the NDVI_3g dataset is a reliable and consistent non-stationary dataset for long-term climate studies.This article presents a non-stationary 1981–2012 AVHRR NDVI_3g time series. The AVHRR NDVI_3g dataset is an improved 8-km normalized difference vegetation index (NDVI) data set derived from AVHRR instruments, which have been flown or are flying on NOAA and EUMETSAT satellites. The dataset is composed of data from two AVHRR instruments: AVHRR/2 (1981–2000) and AVHRR/3 (2000–present). The main challenge in processing AVHRR NDVI data is to properly account for the limitations of the AVHRR instruments, including dual gain introduced in 2000 for AVHRR/3. To overcome these challenges, the authors used Bayesian methods with high-quality SeaWiFS NDVI data to derive AVHRR NDVI calibration parameters. The resulting NDVI values have an error of ±0.005 NDVI units, independent of time, and form a non-stationary climate dataset. The authors used Bayesian analysis to inter-calibrate AVHRR/2 and AVHRR/3 NDVI data, using SeaWiFS data to correct inconsistencies and produce a consistent non-stationary NDVI_3g dataset. The Bayesian approach allows for the estimation of probability distributions and the correction of biases in the AVHRR NDVI data. The resulting NDVI_3g dataset has high spatial and temporal coherence, with a low error of ±0.002 NDVI units. The dataset is used to study climate-related seasonal and inter-annual variability in vegetation. The authors conclude that the NDVI_3g dataset is a reliable and consistent non-stationary dataset for long-term climate studies.