This paper proposes a hardware accelerator for n-dimensional (nD) FastICA methodology, introducing the concept of Vector Cross Product into the Coordinate Rotation Digital Computer (CORDIC) based FastICA to attain high computation speed. The complete FastICA Iteration stage required for computation of the nth weight vector is eliminated by using Vector Cross Product in nD FastICA. Introducing Vector Cross Product in the entirely sequential procedure of CORDIC-based FastICA results in a notable gain in terms of computation time. The proposed methodology has been implemented on hardware using Verilog HDL and synthesized using UMC 180nm technology. It has been functionally verified and validated by applying it for separating human EEG signals. The average improvement in computation time obtained by using this methodology for 4D to 6D FastICA with a case of 1024 samples was found to be 94.61% considering the minimum case of two iterations for nth stage. © 2017 IEEE.