This paper proposes a theory that has the potential to explain the annuity puzzle,i.e., the low demand for annuities in the U.S. and other countries. Specifically, this paper finds that the lack of liquidity of annuities, combined with adverse health shocks, can account for the low demand for annuities. Annuities are less attractive because the elderly find it hard to sell back annuities in case of large medical expenses due to serious health problems. In relation to this, the paper examines the role of the value of life, an intrinsic value attached to a life itself, in the annuity puzzle. If it means a lot to be alive, people would spend more on medical care and hence could demand annuities less. In a series of quantitative analyses,however, I find that the value of life does not reduce the annuity demand much,because more medical care motivated by the value of life can increase the life expectancy, which in turn can raise the annuity demand by increasing the expected payoffs of annuities.