Brain–computer interfaces (BCIs) allow communication between the brain and the external world. This type of technology has been extensively studied. However, BCI instruments with high signal quality are typically heavy and large. Thus, recording electroencephalography (EEG) signals is an inconvenient task. In recent years, system-on-chip (SoC) approaches have been integrated into BCI research, and sensors for wireless portable devices have been developed; however, there is still considerable work to be done. As neuroscience research has advanced, EEG signal analyses have come to require more accurate data. Due to the limited bandwidth of Bluetooth wireless transmission technology, EEG measurement systems with more than 16 channels must be used to reduce the sampling rate and prevent data loss. Therefore, the goal of this study was to develop a multichannel, high-resolution (24-bit), high-sampling-rate EEG BCI device that transmits signals via Wi-Fi. We believe that this system can be used in neuroscience research. The EEG acquisition system proposed in this work is based on a Cortex-M4 microcontroller with a Wi-Fi subsystem, providing a multichannel design and improved signal quality. This system is compatible with wet sensors, Ag/AgCl electrodes, and dry sensors. A LabVIEW-based user interface receives EEG data via Wi-Fi transmission and saves the raw data for offline analysis. In previous cognitive experiments, event tags have been communicated using Recommended Standard 232 (RS-232). The developed system was validated through event-related potential (ERP) and steady-state visually evoked potential (SSVEP) experiments. Our experimental results demonstrate that this system is suitable for recording EEG measurements and has potential in practical applications. The advantages of the developed system include its high sampling rate and high amplification. Additionally, in the future, Internet of Things (IoT) technology can be integrated into the system for remote real-time analysis or edge computing.