We have experimentally demonstrated the effectiveness of beta-gallium oxide (beta-Ga2O3) ferroelectric fin field-effect transistors (Fe-FinFETs) for the first time. Atomic layer deposited (ALD) hafnium zirconium oxide (HZO) is used as the ferroelectric layer. The HZO/beta-Ga2O3 Fe-FinFETs have wider counterclockwise hysteresis loops in the transfer characteristics than that of conventional planar FET, achieving record-high memory window (MW) of 13.9 V in a single HZO layer. When normalized to the actual channel width, FinFETs show an improved ION/IOFF ratio of 2.3x10^7 and a subthreshold swing value of 110 mV/dec. The enhanced characteristics are attributed to the low-interface state density (Dit), showing good interface properties between the beta-Ga2O3 and HZO layer. The enhanced polarization due to larger electric fields across the entire ferroelectric layer in FinFETs is validated using Sentaurus TCAD. After 5x10^6 program/erase (PGM/ERS) cycles, the MW was maintained at 9.2 V, and the retention time was measured up to 3x10^4 s with low degradation. Therefore, the ultrawide bandgap (UWBG) Fe-FinFET was shown to be one of the promising candidates for high-density non-volatile memory devices.