  The neutron pairing correlation and the soft dipole excitation in medium-mass
nuclei near drip-line are investigated from a viewpoint of the di-neutron
correlation. Numerical analyses by means of the coordinate-space HFB and the
continuum QRPA methods are performed for even-even $^{18-24}$O, $^{50-58}$Ca
and $^{80-86}$Ni. A clear signature of the di-neutron correlation is found in
the HFB ground state; two neutrons are correlated at short relative distances
$\lesim 2$ fm with large probability $\sim 50%$. The soft dipole excitation is
influenced strongly by the neutron pairing correlation, and it accompanies a
large transition density for pair motion of neutrons. This behavior originates
from a coherent superposition of two-quasiparticle configurations $[l\times
(l+1)]_{L=1}$ consisting of continuum states with high orbital angular momenta
$l$ reaching an order of $l\sim 10$. It raises a picture that the soft dipole
excitation under the influence of neutron pairing is characterized by motion of
di-neutron in the nuclear exterior against the remaining $A-2$ subsystem.
Sensitivity to the density dependence of effective pair force is discussed.
