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Non-singular Ayon-Beato-Garcia (ABG) spherically symmetric static black hole(BH) with charge to mass ratio $q$ is metric solution of Born-Infeld nonlinearMaxwell-Einstein theory. Central region of the BH behaves as (anti-) de Sitterfor $(|q|>1)~|q|<1 .$ In case of $|q|=1$ the BH central region behaves asMinkowski flat metric. Nonlinear Electromagnetic (NEM) fields counterpartcauses to deviate light geodesics and so light rays will forced to move oneffective metric. In this paper we study weak and strong gravitational lensingof light rays by seeking affects of NEM fields counterpart on image locationsand corresponding magnification. We set our calculations to experimentallyobserved Sgr A$^*$ BH. In short we obtained: For large distances the NEMcounterpart is negligible reaching to linear Maxwell fields. The NEM makesenlarge the BH photon sphere radius as linearly by raising $|q|>1$ but deceasesby raising $|q|\leq1.$ Sign of deflection angle of bending light rays ischanged in presence of NEM effects with respect to ones obtained in absence ofNEM fields. Absolute value of deflection angle raises by increasing $|q|\to1.$Weak image locations decreases (increases) by raising $0<|q|<1$ in presence(absence) of NEM fields. By raising the closest distance of the bending lightrays weak image locations changes from left (right) to right (left) in absence(presence) of NEM fields. Einstein rings radius and corresponding Magnificationcentroid become larger (smaller) in presence (absence) of NEM fields in case ofweak lensing. Angular separation $s$ between the innermost and outermostrelativistic images increases (decreases) by increasing $0<|q|<1$ in absence(presence) of NEM fields. Corresponding magnification $r$ decreases (increases)by raising $0<|q|<1$ in absence (presence) of NEM fields. $s (r)$ raises(decreases) by increasing $|q|>>1.$

Gravitational lensing of charged Ayon-Beato-Garcia black holes and non-linear effects of Maxwell fields