This paper proposes an n-dimensional (nD) Hybrid FastICA methodology introducing the concept of Vector Cross Product into the Coordinate Rotation Digital Computer (CORDIC) based FastICA to attain high computation speed. The use of Vector Cross Product into the nD FastICA eliminates the complete Iteration stage required for computation of the nth weight vector. This introduction of Vector Cross Product into the entirely sequential procedure of CORDIC-based FastICA provides significant gain in terms of computation time. The functionality of the proposed methodology is validated by applying it on random signals, audio signals and biomedical signals. Subsequently, the hardware architecture has also been implemented and validated. The average improvement in computation time obtained by employing this methodology for 4D to 7D FastICA with a typical case of 1024 samples was found to be a minimum of 77% for nth vector computation, which further increases with increase in the iterations required for nth vector computation and the frame-length. Copyright © 2018 American Scientific Publishers All rights reserved.