  Recently, inspired by Eddington's theory, an alternative gravity called
Eddington-inspired Born-Infeld gravity was proposed by Ba$\tilde{\text{n}}$ados
and Ferreira. It is equivalent to Einstein's general relativity in vacuum, but
deviates from it when matter is included. Interestingly, it seems that the
cosmological singularities are prevented in this theory. Based on the new
theory, we investigate a thick brane model with a scalar field presenting in
the five-dimensional background. A domain wall solution is obtained, and
further, we find that at low energy the four-dimensional Einstein gravity is
recovered on the brane. Moreover, the stability of gravitational perturbations
is ensured in this model.
