Based on utility theory, this paper firstly combined different utility functions with risk aversion coefficient and constructed different kinds of optimizing problems for hedgers to hedge for stochastic-payment-typed contingent claim, and then, by the aid of dynamic programming theory, effective multi-stage hedging strategy is proposed for different risk-averse hedgers. Lastly, the research results that the optimal hedging ratios for three kinds of utility functions are equivalent and do not relate to the risk aversion coefficient.