  Pion superfluid phase transition under external magnetic field including the
inverse magnetic catalysis (IMC) effect is investigated by the Pauli-Villars
regularized NJL model. Based on the Goldstone's theorem, we apply the massless
Goldstone boson ($\pi^+$ meson) to determine the onset of pion superfluid
phase. The inverse magnetic catalysis effect is introduced by the magnetic
field dependent coupling $G(eB)$, which is a decreasing function of magnetic
field. At fixed temperature and baryon chemical potential, the critical isospin
chemical potential for pion superfluid phase transition including IMC effect
increases as the magnetic field grows, which is similar as the case without IMC
effect. This demonstrates that magnetic field disfavors the pion superfluid
phase when considering or ignoring IMC effect. The critical isospin chemical
potential at fixed magnetic field, temperature and baryon chemical potential is
shifted to higher value by the IMC effect. Since it is more difficult to form
pion superfluid with weaker coupling.
