We conducted $^{77}$Se-nuclear magnetic resonance studies of the iron-based superconductor FeSe in magnetic fields of 0.6 to 19 T to investigate the superconducting and normal-state properties. The nuclear spin-lattice relaxation rate divided by the temperature $(T_1T)^{-1}$ increases below the structural transition temperature $T_mathrm{s}$ but starts to be suppressed below $T^*$, well above the superconducting transition temperature $T_mathrm{c}(H)$, resulting in a broad maximum of $(T_1T)^{-1}$ at $T_mathrm{p}(H)$. This is similar to the pseudogap behavior in optimally doped cuprate superconductors. Because $T^*$ and $T_mathrm{p}(H)$ decrease in the same manner as $T_mathrm{c}(H)$ with increasing $H$, the pseudogap behavior in FeSe is ascribed to superconducting fluctuations, which presumably originate from the theoretically predicted preformed pair above $T_mathrm{c}(H)$.