This paper focused on accurate singular value computation for fg-Vandermonde-type (fg-VT) matrices, which are widely used in interpolation and other applications. We first derived explicit expressions for the initial minors of fg-VT matrices, then presented parametrization formulas for their corresponding matrices. Based on these results, we proposed an algorithm with high relative accuracy for computing all singular values. Additionally, we developed perturbation theory and error analysis to further assess the accuracy of our approach. Finally, numerical experiments were conducted to verify high accuracy of the algorithm.