A field-programmable gate array (FPGA)-based hardware architecture is proposed and utilized for prediction of neuronal population firing activity. The hardware system adopts the multi-input multi-output (MIMO) generalized Laguerre-Volterra model (GLVM) structure to describe the nonlinear dynamic neural process of mammalian brain and can switch between the two important functions: estimation of GLVM coefficients and prediction of neuronal population spiking activity (model outputs). The model coefficients are first estimated using the in-sample training data; then the output is predicted using the out-of-sample testing data and the field estimated coefficients. Test results show that compared with previous software implementation of the generalized Laguerre-Volterra algorithm running on an Intel Core i7-2620M CPU, the FPGA-based hardware system can achieve up to 2.66×10(3) speedup in doing model parameters estimation and 698.84 speedup in doing model output prediction. The proposed hardware platform will facilitate research on the highly nonlinear neural process of the mammal brain, and the cognitive neural prosthesis design.