The green bond market has dramatically expanded especially in Europe but severe liquidity issues may undermine its rapid development. If few studies have assessed the implied liquidity risks for investors in terms of liquidity premium, none of them have specifically analysed its behavior across bond maturities. To fill this gap, this paper studies the term structure of the liquidity premium of the green bond market. We find that the sizes of short-term and long-term premia are close to those estimated on the German government bond market. We show that those premia are affected by economic factors and by spillover effects between them, which contribute to the U-Shape of the liquidity premium. Finally, we detect a liquidity clientele effect on the ask side impacting the liquidity premium, which implies a maturity segmentation i.e., high-risk (resp. low-risk) investors buy short-term (resp. long-term) green bonds and hold them until maturity. Taken together, our results deliver valuable insights on investors' strategies in the green bond market. Quite importantly, green bond investors prefer to opt for buy and hold strategies because they are compensated for higher liquidity risks along the entire maturity spectrum.