  The isospin equilibration process in multinucleon transfer reaction is
investigated by using the improved quantum molecular dynamics model. The
collision processes of $^{124}$Xe+$^{208}$Pb at near-barrier energy are studied
with different symmetry energy coefficients. We find that neutrons transfer
happens earlier than protons. The large symmetry energy promote the transfer of
neutrons. The neutron flow from the target to projectile is along the
low-density path of neck. The isospin equilibration process in
$^{58}$Ni+$^{208}$Pb reaction is also investigated and compared with available
experimental data. It shows that $N/Z$ values of the projectile-like products
increase rapidly with increasing mass transfer. The complete isospin
equilibration events are located in the region of $120<A<150$ which are
produced in symmetric fission-type reactions.
