  The pseudogap effect of underdoped high-$T_c$ superconductors is studied in
the U(1) gauge theory of the t-J model including the spinon pairing
fluctuation. The gauge fluctuation breaks the long range correlation between
the spinon pairs. The pairing fluctuation, however, suppresses significantly
the low-lying gauge fluctuations and leads to a stable but phase incoherent
spin gap phase which is responsible for the pseudogap effects. This quantum
disordered spin gap phase emerges below a characteristic temperature $T^{*}$
which is determined by the effective potential for the spinon pairing gap
amplitude. The resistivity is suppressed by the phase fluctuation below $%
T^{*}$, consistent with experiments.
