  Magnetic field effect on pion superfluid phase transition is investigated in
frame of a Pauli-Villars regularized NJL model. Instead of directly dealing
with charged pion condensate, we apply the Goldstone's theorem (massless
Goldstone boson $\pi^+$) to determine the onset of pion superfluid phase, and
obtain the phase diagram in magnetic field, temperature, isospin and baryon
chemical potential space. At weak magnetic field, it is analytically proved
that the critical isospin chemical potential of pion superfluid phase
transition is equal to the mass of $\pi^+$ meson in magnetic field. The pion
superfluid phase is retarded to higher isospin chemical potential, and can
survive at higher temperature and higher baryon chemical potential under
external magnetic field.
