The electrodynamic reaction sphere is a novel actuator for the spacecraft attitude control subsystem. This paper proposes a neural network inverse based decoupling control scheme to actualize the omnidirectional rotation of the electrodynamic reaction sphere which has strong multivariable nonlinear coupling features due to the induction-based drive. And an integrated electromagnetic torque model of the reaction sphere is firstly derived from the electromagnetic field analysis and modified with the finite element analysis method. Then based on the integrated torque model, a back propagation feedforward neural network is constructed and trained to approach the inverse dynamics which transforms the original system into a pseudo-linear system. Furthermore, an additional PI controller is introduced to achieve good control performance against the unmodelled dynamics. Finally, the effectiveness of the proposed method is validated by simulations.