It has been a long-standing question whether cosmic rays promote the triggering of lightning and how cosmic-ray air showers interact with the electric field of thunderclouds. The strong electric field in the thunderclouds accelerates electrons to the relativistic regime, of which seed electrons are thought to be supplied from cosmic-ray air shower. Such relativistic electrons emit bremsstrahlung photons in gamma rays, which have been detected by on-ground measurements called gamma-ray glows. Low-altitude winter thunderstorm in Japan provides an ideal environment for observations of gamma-ray glows. We newly launched the citizen science ``Thundercloud Project" to construct a multi-point radiation mapping campaign for glows from winter thunderstorms around Kanazawa, Japan. We developed a new handy radiation monitor and shipped about 60 detectors to citizen supporters. The radiation data are stored in the microSD cards in the detectors, and a part of them is remotely sent to the web server so that researchers and supporters can watch the real-time data. In addition, an automatic alert is sent to public Twitter from the server when a glow is detected. The purpose of this project is (1) to characterize the methodological condition of electron acceleration, (2) to investigate whether accelerated relativistic electrons can enhance the chance of the initiation of lightning discharges, and (3) to find a new way of the citizen science to join in the cutting edge science in the physics field. Here we report this growing citizen science project and examples of successful gamma-ray glow observations. Our first scientific result from this citizen science project was published in Tsurumi et al., GRL 2023, where we reported lightning discharges started in or near the electron acceleration site of a gamma-ray glow.