This paper studied the pricing problem of European option under an incomplete market on the basis of consumption utility indifference. The conclusions of Black-Scholes models were recovered even for a general utility function. In contrast to complete markets, it is found that the utility indifference price for CARA utility may decrease if the volatility of the underlying asset or the lifetime of the option increases under the incomplete market. The risk attitude of an investor has effects on option prices only if there is idiosyncratic risk exposed in the option. The smaller the idiosyncratic risk exposed in the option, the weaker the effect of the risk attitude on the consumption utility indifference price. Especially, if there is no idiosyncratic risk exposed in the option, the risk attitude will make no impact on option prices.