We present results from the NASA GISS ModelE2.1‐G‐CC Earth System Model with coupled climate‐carbon cycle simulations that were submitted to the sixth phase of the Coupled Model Intercomparison Project (CMIP6) Coupled Climate‐Carbon Cycle MIP (C4MIP). Atmospheric CO₂ concentration and carbon budgets for the land and ocean in the historical simulations were generally consistent with observations. Low simulated atmospheric CO₂ concentrations during 1850–1950 were due to excess uptake from prescribed land cover change, which erroneously replaced arid shrublands with higher biomass crops, and assumed high 2004 LAI values in vegetated lands throughout the historical simulation. At the end of the historical period, slightly higher simulated CO₂ than observed resulted from the land being an insufficient net carbon sink, despite the net effect of CO₂ fertilization and warming‐induced increases to leaf photosynthetic capacity. The global ocean carbon uptake agreed well with the observations with the largest discrepancies in the low latitudes. Future climate projection at 2091–2100 agreed with CMIP5 models in the northward shift, of temperate deciduous forest climate and expansion across Eurasia along 60°N latitude, and dramatic regional biome shifts from drying and warming in continental Europe. Carbon feedback parameters were largely similar to the CMIP5 model ensemble. For our model, the variation of land feedback parameters within the uncertainty arises from the fertilization feedback being less sensitive due to lack of increased vegetation growth, and the comparably more negative ocean carbon‐climate feedback is due to the large slowdown of the Atlantic overturning circulation.