  The pion superfluidity phase transition at $T-\mu_I$ and $\mu_q-\mu_I$ planes
are studied in the framework of Dyson-Schwinger equations. The rainbow
truncation and Gaussian effective gluon propagator are employed to calculate
pion condensate, $\langle\pi\rangle$, as a function of $\mu_I$ at finite $T$
and $\mu_q$. At $T=(0, 80, 113, 120)$~MeV, the $\langle\pi\rangle$ keeps zero
when $\mu_I$ is less than a critical value $\mu_{Ic}(T)$. The
$\langle\pi\rangle$ at $T=113$~MeV agrees with the lattice QCD result. At the
$T-\mu_I$ plane, the pion superfluid phase appears at low temperature and high
isospin chemical potential region. At finite $\mu_q$, $\langle\pi\rangle$
varying with $\mu_I$ almost coincide for $\mu_q<400$~MeV. At $\mu_q-\mu_I$
plane, the pion superfluid phase appears at $\mu_I\gtrsim m_\pi$ when
$\mu_q<400$~MeV.
