Brain-computer interface (BCI) is a system that may benefit people with severe motor disabilities by allowing them to communicate using their brain's signals. However, trends in BCI implementation use large and heavy platforms, such as personal computers (PCs), which limit full integration with portable devices. Due to its parallelism, reconfigurable features, and capabilities to perform multiple channel processing, the Field-Programmable Gate Array (FPGA) platform is suitable for electroencephalography (EEG) signal processing. This paper presents the design and implementation of an FPGA-based BCI embedded system for eye state classification in real-time. The system was implemented using Xilinx Artix-7 family FPGA. The designed system filtered EEG signals using FIR filters and the pattern features were calculated using Power Spectral Density (PSD). Furthermore, Linear Discriminant Analysis (LDA) was used to classify EEG data related to the eye state. The proposed system was tested using recorded data from a subject acquired by the open-source biosensing board Cyton for offline and online evaluation. The system achieved an accuracy of 81.1% during real-time sessions. Finally, the results show the execution time, resources, and power consumption of the designed system.