The uncertainty about the future mortality developments is referred to as longevity risk. This paper quanti…es the size of longevity risk premium which should be priced in various longevity-linked securities and annuity contracts. The goal of this project is to tackle the pricing di¢ culty emerged during the market innovation of the potential longevity-linked securities. Based on the equivalent utility pricing principle, we obtain the minimum risk premium required by the longevity insurance seller and the maximum acceptable risk premium by the longevity insurance buyer. Our estimated risk premium is consistent with the limited observations in the market. We show that the size of the risk premium depends on the …nancial position of the seller and buyer, and the availability of the natural hedges. One important implication for the market development of longevity-linked securities is that multiple sellers are required instead of a single seller. The paper also shows that the availability of natural hedge has signi…cant impact on the longevity risk premium required. Longevity risk is modelled by Lee-Carter (1992) model, and estimated according to the U.K. and the Dutch mortality data.