Fast Radio Burst (FRB) is a high-energy astrophysical phenomenon of short duration that plays a significant role in studying the distribution and evolution of matter in the universe. FRB can only be observed through radio telescopes, which produce extensive amounts of observational data, making the search for FRB challenging. Traditional techniques for searching FRB are computationally expensive, time-consuming, and may fail to detect weak signals, leading to decreased effectiveness. Consequently, machine learning algorithms are employed to mitigate the challenges of searching FRB. This poses a challenge since only a limited number of incomplete or inadequate FRB datasets are available for machine learning algorithms. Hence, providing substantial and authentic datasets is crucial in aiding machine learning algorithms to detect FRB.The FAST dataset for Fast Radio bursts EXploration (FAST-FREX) is obtained from observation data collected by the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Our dataset comprises 600 positive samples of observed FRB signals from multiple sources and 1000 negative samples of noise and Radio Frequency Interference (RFI). We created our dataset by using the observational data of FRB20121102, FRB20180301 and FRB20201124. These observations gathered data using 4096 frequency channels over 1.05 GHz to 1.45 GHz, with 0.122 MHz frequency resolution. These channels recorded four polarization signals. FRB20121102 has a 98.304 μs sampling rate, while others have a 49.152 μs sampling rate. The raw observation data was stored in FITS format and divided into blocks of 128 or 256 time samples. The samples were recorded in consecutive lines (or sub-integrations) in a file with 1024 samples per sub-integration.The dataset comprises two file types: sample files and parameter description files. The sample files, stored in FITS format, contain pre-cropped observation data. Among them are 600 positive sample files containing FRB signals and 1000 negative sample files containing RFI and noise. The FRB20121102 sample file has a time sampling point of 60 * 1024, while other sources' sample files have 120 * 1024. Moreover, the sample file's number of polarization channels is reduced to one, which differs from the original data. The size of each file is approximately 244 MB or 488 MB, depending on its time sampling rate. Meanwhile, parameter description files are stored in CSV format to record various FRB parameters for each positive...