  We examine the gravitational lensing phenomenon caused by photon spheres in
the Born-Infeld naked singularity spacetime, where gravity is coupled with
Born-Infeld electrodynamics. Specifically, our focus lies on relativistic
images originating from a point-like light source generated by strong
gravitational lensing near photon spheres, as well as images of a luminous
celestial sphere. It shows that Born-Infeld naked singularities consistently
exhibit one or two photon spheres, which project onto one or two critical
curves on the image plane. Interestingly, we discover that the nonlinearity
nature of the Born-Infeld electrodynamics enables photons to traverse the
singularity, leading to the emergence of new relativistic images within the
innermost critical curve. Furthermore, the presence of two photon spheres
doubles the number of relativistic images compared to the scenario with only a
single photon sphere. Additionally, the transparency inherent to Born-Infeld
naked singularities results in the absence of a central shadow in the images of
celestial spheres.
