A permanent magnet spherical actuator is an electromagnetic device characterized by achieving multi-degree-of-freedom rotations in one driving unit. Analytical magnetic field modeling of the rotor array is needed for the design, performance analysis and optimization of the spherical actuator. This paper presents an analytical method to formulate the complex magnetic field distribution of rotor array with cylindrical permanent magnets in 3D spherical space. This method combines the current model by toroidal functions and transformation method, thus the magnetic field can be calculated efficiently with reasonable accuracy in order for further design optimization and real-time control. The analytical magnetic model of the permanent magnet rotor array is validated with the numerical finite element method by Ansoft Maxwell and experimental measurement.