The emphasis of portfolio decision-making is placed on how to obtain the optimal solution of portfolio allocation in recent years. The objective for most of programming models, so called either the return model or the risk model, is to maximize the profit or to minimize the cost for portfolio selection based on mean-variance (MV) theorem proposed by Markowitz. However, both two objectives must be taken into consideration at the same time instead of trade-off between risk and return in the real situations. In general, these two objectives are not crisp under uncertainty environment from the point of view of the investors. In this paper, a method of portfolio selection is proposed to arrive at dealing with optimizing risk-return structure of a portfolio simultaneously in fuzzy terms, named fuzzy multi-goal portfolio (FMGP) decision-making model. The FMGP decision making model here is applied to analyze the weighting for the underlying of a portfolio with the aspiration-level using fuzzy membership functions (FMFs) to obtain feasible solutions. Genetic algorithm (GA) is also employed here to tackle the curse of computation for a large-scale portfolio. The evidence from Morgan Stanley country indices (MSCI) portfolios shows the viability and effectiveness for the investment decision-making under uncertainty environment.