We use a DSGE model to study the effectiveness of green-asset purchases by the central bank (Green QE), along the transition to a carbon-free economy driven by an emission tax, abstracting from price stability considerations. We find that Green QE helps to further reduce emissions, especially in the early stage of the transition. We find that a crucial parameter to determine the effectiveness of Green QE is the elasticity of substitution between the brown and the green good: the higher the elasticity the stronger the impact of the policy on emissions