Cosmic rays interact with the Earth's atmosphere to produce 14C, which can be absorbed by trees. Therefore, rapid increases of 14C in tree rings can be used to probe previous cosmic-ray events. By this method, three 14C rapidly increasing events have been found. Plausible causes of these events include large solar proton events, supernovae, or short gamma-ray bursts. However, due to the lack of measurements of 14C by year, the occurrence frequency of such 14C rapidly increasing events is poorly known. In addition, rapid increases may be hidden in the IntCal13 data with five-year resolution. Here we report the result of 14C measurements using an ancient buried tree during the period between BC 3388 and 3358. We found a rapid increase of about 9‰ in the 14C content from BC 3372 to BC 3371. We suggest that this event could originate from a large solar proton event.