  A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by D.
Glavan and C. Lin [Phys. Rev. Lett. 124, 081301 (2020)], which is intended to
bypass the Lovelock's theorem and to yield a non-trivial contribution to the
four-dimensional gravitational dynamics. However, the validity and consistency
of this theory has been called into question recently. We study a static and
spherically symmetric black hole charged by a Born-Infeld electric field in the
novel four-dimensional Einstein-Gauss-Bonnet gravity. It is found that the
black hole solution still suffers the singularity problem, since particles
incident from infinity can reach the singularity. It is also demonstrated that
the Born-Infeld charged black hole may be superior to the Maxwell charged black
hole to be a charged extension of the Schwarzschild-AdS-like black hole in this
new gravitational theory. Some basic thermodynamics of the black hole solution
is also analyzed. Besides, we regain the black hole solution in the regularized
four-dimensional Einstein-Gauss-Bonnet gravity proposed by H. L\"u and Y. Pang
[arXiv:2003.11552].
