  Non-singular Ayon-Beato-Garcia (ABG) spherically symmetric static black hole
(BH) with charge to mass ratio $q$ is metric solution of Born-Infeld nonlinear
Maxwell-Einstein theory. Central region of the BH behaves as (anti-) de Sitter
for $(|q|>1)~|q|<1 .$ In case of $|q|=1$ the BH central region behaves as
Minkowski flat metric. Nonlinear Electromagnetic (NEM) fields counterpart
causes to deviate light geodesics and so light rays will forced to move on
effective metric. In this paper we study weak and strong gravitational lensing
of light rays by seeking affects of NEM fields counterpart on image locations
and corresponding magnification. We set our calculations to experimentally
observed Sgr A$^*$ BH. In short we obtained: For large distances the NEM
counterpart is negligible reaching to linear Maxwell fields. The NEM makes
enlarge the BH photon sphere radius as linearly by raising $|q|>1$ but deceases
by raising $|q|\leq1.$ Sign of deflection angle of bending light rays is
changed in presence of NEM effects with respect to ones obtained in absence of
NEM 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 light
rays weak image locations changes from left (right) to right (left) in absence
(presence) of NEM fields. Einstein rings radius and corresponding Magnification
centroid become larger (smaller) in presence (absence) of NEM fields in case of
weak lensing. Angular separation $s$ between the innermost and outermost
relativistic 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 $|q|>>1.$
