This paper presents a three-dimensional (3D) massive multiple-input and multiple-output (MIMO) antenna array model, which includes the spherical array assumption and geometric properties for future fifth generation (5G) wireless communications. A parametric approximation algorithm is developed for estimating the spatial fading correlations (SFCs) and channel capacities of the 3D massive MIMO antenna array systems under different power angular spectrum (PAS). The relationship between correlation with the spacing of antenna arrays and angular parameters was classified. The results show that the simulation values of the approximate method fit the theoretical calculation very well, thereby validating the feasibility of the proposed 3D large-scale massive MIMO model.