One important step towards the cognitive neural prosthesis design is to achieve real-time prediction of neuronal firing pattern. An FPGA-based hardware computational platform is designed to guarantee this hard real-time signal processing requirement. The proposed platform can work in dual modes: generalized Laguerre-Volterra model parameters estimation and output prediction, and can switch between these two important system functions. Compared with the traditional software-based platform implemented in C, the hardware platform achieves better efficiency in doing the biocomputations by up to thousandfold speedup in this process.