A thermionic RF gun for an accelerator-based terahertz source has been commissioned at Electron Light Science Centre, Tohoku University. Recently we constructed the measurement system to obtain the momentum distribution of the extracted beam from the RF gun. The system consists of the analyser magnet, tungsten beam slit followed by a Faraday cup and a Hall probe for the realtime magnetic field measurement. The momentum resolution of the spectrometer is estimated to be about 0.15 %, which will be sufficient to analyse the detailed distribution of highest energy part for the extracted electrons from the gun. The preliminary results of measured momentum spectrum and the current status of the terahertz source project are presented.