Mutual funds become one of the major channels for investors because of professional management, and the advantage of enjoying profit and sharing risks. The goal of this study is applying Grey prediction, radial basis function neural network (RBFNN) and Grey-RBFNN to predict the net asset value (NAV) of single nation equity funds. Grey model is a simple approach with acceptable prediction accuracy whereas radial basis function neural network is a tedious manipulation with high prediction accuracy. A recursive algorithm with on-line learning capability combining Grey and RBFNN (GM-RBFNN) is proposed and tested. This new algorithm utilizes the GM(I,I) prediction as one of the RBFNN inputs without increasing any nodes in the hidden layer. Prediction performances of all three algorithms are compared by using data of three single nation equity funds, JF Taiwan Fund, JF Japan New Generation Fund, and JPM New America Trust Fund from JP Morgan Asset Management, Taiwan. The CM-RBFNN is slightly better than RBFNN algorithm. The Error Index (EI) of learning phase and test phase are less than 0.055 and 0.050 respectively. For the Grey prediction model, the Error Index (EI) is less than 0.065.