  We investigate how the cosmological constraints from SNe Ia are improved by
including the effects of weak-lensing convergence. To do so, we introduce the
lognormal function as the convergence PDF modeling the lensing scatter of SN Ia
magnitude, and apply a sample selection for SNe Ia to avoid strongly lensed
samples. Comparing with the contribution of other uncertainties (e.g., the
intrinsic magnitude scatter), we find that the lensing effect is dominant at $z
> 1$. Then forecasting the parameter constraints for the Wide-Field InfraRed
Survey Telescope survey, we show that considering the weak-lensing effect, the
constraints on the density parameters $\Omega_m$ or $\Omega_{\Lambda}$, and the
dark energy equation of state $w$ are improved, especially for SNe Ia samples
at higher redshift $z > 1$. Furthermore, we see that the degeneracy between the
total mass of neutrino $\Sigma m_{\nu}$ and the (cold) dark matter density
parameter $\Omega_{c}$ can be resolved.
