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Ground data from the National Forest and Soil Inventory of Mexico (INFyS) were used to calibrate a maximum entropy (MaxEnt) algorithm to generate forest biomass (AGB), its associated uncertainty, and forest probability maps. The input predictor layers for the MaxEnt algorithm were extracted from the moderate resolution imaging spectrometer (MODIS) vegetation index (VI) products, ALOS PALSAR L-band dual-polarization backscatter coefficient images, and the Shuttle Radar Topography Mission (SRTM) digital elevation model. A Jackknife analysis of the model accuracy indicated that the ALOS PALSAR layers have the highest relative contribution (50.9%) to the estimation of AGB, followed by MODIS-VI (32.9%) and SRTM (16.2%). The forest cover mask derived from the forest probability map showed higher accuracy (κ = 0.83) than alternative masks derived from ALOS PALSAR (κ = 0.72–0.78) or MODIS vegetation continuous fields (VCF) with a 10% tree cover threshold (κ = 0.66). The use of different forest cover masks yielded differences of about 30 million ha in forest cover extent and 0.45 Gt C in total carbon stocks. The AGB map showed a root mean square error (RMSE) of 17.3 t C ha− 1 and R2 = 0.31 when validated at the 250 m pixel scale with inventory plots. The error and accuracy at municipality and state levels were RMSE = ± 4.4 t C ha− 1, R2 = 0.75 and RMSE = ± 2.1 t C ha− 1, R2 = 0.94 respectively. We estimate the total carbon stored in the aboveground live biomass of forests of Mexico to be 1.69 Gt C ± 1% (mean carbon density of 21.8 t C ha− 1), which agrees with the total carbon estimated by FAO for the FRA 2010 (1.68 Gt C). The new map, derived directly from the biomass estimates of the national inventory, proved to have similar accuracy as existing forest biomass maps of Mexico, but is more representative of the shape of the probability distribution function of AGB in the national forest inventory data. Our results suggest that the use of a non-parametric maximum entropy model trained with forest inventory plots, even at the sub-pixel size, can provide accurate spatial maps for national or regional REDD + applications and MRV systems.