Global and regional land carbon storage has been significantly affected by increasing atmospheric CO2 concentration and climate change. Based on fully coupled climate-carbon-cycle simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5), we investigate sensitivities of land carbon storage to rising atmospheric CO2 concentration and climate change over the world and 21 regions during the 130 years. Overall, the simulations suggest that consistently spatial positive effects of the increasing CO2 concentrations on land carbon storage are expressed with a multi-model averaged value of 1.04 PgC per ppm. The stronger positive values are mainly located in the broad areas of temperate and tropical forest, especially in Amazon basin and western Africa. However, large heterogeneity distributed for sensitivities of land carbon storage to climate change. Climate change causes decrease in land carbon storage in most tropics and the Southern Hemisphere. In these regions, decrease in soil moisture (MRSO) and enhanced drought somewhat contribute to such a decrease accompanied with rising temperature. Conversely, an increase in land carbon storage has been observed in high latitude and altitude regions (e.g., northern Asia and Tibet). The model simulations also suggest that global negative impacts of climate change on land carbon storage are predominantly attributed to decrease in land carbon storage in tropics. Although current warming can lead to an increase in land storage of high latitudes of Northern Hemisphere due to elevated vegetation growth, a risk of exacerbated future climate change may be induced due to release of carbon from tropics.