•The reasonability of Chinese government’s CO2 emissions reduction allocation plan is examined.•The stochastic convergence and β-convergence are tested using the provincial panel data.•Both fixed effects and Generalized Method of Moments (GMM) estimators are utilized.•The provinces with high carbon intensity tend to experience faster reduction in carbon intensity, and vise versa. To curb CO2 emissions, the Chinese government has announced ambitious goals to reduce the CO2 intensity of GDP, and the total target has been allocated to all Chinese provinces during the twelfth “Five-year Plan” period (2011–2015). Although setting the target allocation plan is an efficient way to achieve this goal, some key questions, including how the plan is designed, remained unanswered. From an economic perspective, this requires us to test for the existence of convergence in the CO2 intensity of GDP because the convergence is one of the most important intrinsic economic characteristics that policy makers should take into account: if the convergence exists, the provinces with a higher CO2 intensity of GDP tend to experience a more rapid reduction in the intensity and therefore could share a heavier burden of the intensity reduction. The existence of stochastic convergence and β-convergence is verified by employing different estimation methods and using various estimation specifications. As a result, the direct policy implication is that provinces with high CO2 intensity should be assigned tougher reduction targets to cut CO2 intensity at higher speeds, while the provinces with low carbon intensity should be allowed to reduce the CO2 intensity at a relatively lower speed. Because some social and economic indicators such as GDP per capita, industrial structure and population density may influence CO2 intensity, the policy makers should take all these factors into consideration to design reasonable reduction target allocation plan.