  In this paper, we study the generation of a large scale magnetic field with
amplitude of order $\mu$G in an inflationary model which has been introduced in
hep-th/0310221. This inflationary model based on existence of a speed limit for
inflaton field. Generating a mass for inflaton at scale above the $\phi_{IR}$,
breaks the conformal triviality of the Maxwell equation and causes to originate
a magnetic field during the inflation. The amplitude strongly depends on the
details of reheating stage and also depends on the e-foldings parameter N. We
find the amplitude of the primordial magnetic field at decoupling time in this
inflationary background using late time behavior of the theory.
