This paper develops a model of the lender of last resort (LOLR) from a Central Bank (CB) viewpoint. The model in a static setting suggests that the CB would only rescue banks which are above a threshold size, consistent with the insight of “too big to fail”. In a dynamic setting, CB’s optimal policy in liquidity support depends on the trade off between contagion and moral hazard effects. Our results show that contagion is the key factor affecting CB’s incentives in providing LOLR and they also provide a rationalization for “constructive ambiguity”.