  In this paper we develop a new method that is different from Schwinger proper
time method to deduce the fermion propagator with a constant external magnetic
field. In the NJL model, we use this method to find out the gap equation at
zero and non-zero temperature, and give the numerical results and phase diagram
between magnetic field and temperature. Beside these, we also introduce current
mass to study the susceptibilities, because there is a new parameter (the
strength of external magnetic field) in this problem, corresponding this new
parameter, we have defined a new susceptibility $\chi_B$ to compare with the
other two susceptibilities $\chi_c$ (chiral susceptibility) and $\chi_T$
(thermal susceptibility), and all of the three susceptibilities show than when
current mass is not zero, the phase transition is a crossover, while for
comparison, in the chiral limit, the susceptibilities show a second order phase
transition. At last, we give out the critical coefficients of different
susceptibilities in the chiral limit.
