In this work, we study the anisotropic inflationary models . In these models,  an abelian gauge field  non-minimally coupled to the inflaton field plays a role in the inflation dynamicIn a gauge field,the backgroundanswer is anisotropic, in the form of metric Bianchi. In order for the model to be consistent with the observations, the level of anisotropy should be small. The anisotropy power spectrum is obtained by calculating  cosmological perturbation using  formalism. We show that the  criticism levelled in [4] does not apply and we can repeat the calculations in the non-absorbence by calculating the anisotropy spectrum. Using the constraint on the quadrupole anisotopy, we show that the contribution of the gauge field to total energy density should be very small