  In this paper, we study quantum corrections to the temperature and entropy of
a regular Ay\'{o}n-Beato-Garc\'{\i}a-Bronnikov black hole solution by using
tunneling approach beyond semiclassical approximation. We use the first law of
black hole thermodynamics as a differential of entropy with two parameters,
mass and charge. It is found that the leading order correction to the entropy
is of logarithmic form. In the absence of the charge, i.e., $e=0$, these
corrections approximate the corresponding corrections for the Schwarzschild
black hole.
