This study analyzes the effect of the uncertain indemnity on the insurance demand. At first, insurance demand depends on the policyholder’s prudence. When the policyholder who is sufficiently prudent purchases insurance with fair premium even though the indemnity is uncertain. Second, the policyholder may purchase partial insurance depending on the level of prudence even when the premium is fair. Third, more risk averse policyholder purchases more insurance following the level of ARA and RRA. Fourth, when the probability distribution of indemnity uncertainty shifts following MPS(Mean Preserving Spread), the demand of insurance may increase depending on the Absolute and Relative Prudence, ARA and RRA. Fifth, the variance and the lower bound of indemnity uncertainty and prudence affect the demand of insurance when the loss size increases. Lastly, insurance may be normal goods when the policyholder has an utility function with non increasing ARA.