We utilize stochastic dominance approach for the investment decision making about how to choose index funds under uncertainty. It is found that the Small & Medium Board Index Fund provides greedy investors greater expected utility as well as brings risk-averse investors less risk, and thus it is the preferred choice of investment decision-making. Besides, the stochastic dominance procedure displays good potential usefulness among the fields of products evaluating, investment decision-making, R&D and marketing etc.