This paper presents a method to construct a profitable portfolio of mutual funds for investors. This method comprises two stages. In the first stage, the DEA, Sharpe and Treynor indices of mutual funds and the monthly rates of return (ROR) of mutual funds are used to select a mutual fund portfolio. In the second stage, the linear regression model, the Fruit Fly Optimization Algorithm (FOA) and the General Regression Neural Network (GRNN) are used to construct a prediction model for the net asset values of each of the constituent mutual funds of the portfolio. The trade decision of a selected mutual fund is then made based on the rise or fall of its net asset value. The empirical results showed that, compared to other combinations, the combination of using Sharpe index for portfolio selection and the GRNN optimized with FOA for net asset value prediction offered the best accumulated return rate for the mutual fund portfolio investment.