  On the basis of $t$-matrix approximation, we study the superconductivity in
the tight-binding model with d-wave attraction. The low-lying collective modes
are considered as the predominant long-range fluctuations in the system. The
Green's function is obtained as an analytic solution to a cubic equation. The
superconducting order parameter and the transition temperature are
substantially reduced from the values of the mean-field theory. The results for
the pseudogap parameter at $T_c$ are compared with experiments. The calculated
phase boundary of the superconductivity can reasonably describe the experiment
results for the cuprates. The results for density of states are presented.
