Within the framework of the standard quantum electrodynamics , we compute contribution of vacuum polarization at one-loop order to the power spectrum of the magnetic field on inflationary ( de Sitter ) background . It is found that the one-loop term exhibits the infrared secular growth that is proportional to the number of e -folds . The use of the dynamical renormalization group method , which amounts to partial resummation of higher loop diagrams , shows that the resummed power spectrum is free from the secular growth and the loop effect only changes the power from ( k / a ) ^ { 4 } at the tree level to { ( k / a ) } ^ { 4 - \nu } , where \nu represents the contribution from vacuum polarization . The parameter \nu , being proportional to the square of the gauge coupling constant as well as the number of fermion species , is a simple function of a ratio of fermion mass to the Hubble parameter and is positive irrespective of the fermion mass . Thus , the loop effect always enhances the infrared magnetic field strength . We find that \nu \simeq 5 \times 10 ^ { -3 } is the possible maximum contribution to \nu from a single fermion . This estimate suggests that either large number of fermion species or large coupling constant is a necessary condition for the loop effect to be responsible for the seed of the cosmic magnetic fields .