  In the hole-doped cuprate superconductors, the superconducting transition
temperature $T_c$ exhibits a dome-like feature against the doping rate. By
contrast, recent experiments reveal that $T_c$ in the electron-doped systems
monotonically increases as the doping is reduced, at least up to a very small
doping rate. Here we show that this asymmetry is reproduced by performing a
two-particle self-consistent analysis for the three-band model of the CuO$_2$
plane. This is explained as a combined effect of the intrinsic electron-hole
asymmetry in systems comprising Cu3$d$ and O2$p$ orbitals and the
band-filling-dependent vertex correction.
