  We investigate the scalar and the tensor perturbations of the $\varphi^2$
inflation model in the strong-gravity limit of Eddington-inspired Born-Infeld
(EiBI) theory. In order to consider the strong EiBI-gravity effect, we take the
value of $\kappa$ large, where $\kappa$ is the EiBI theory parameter. The
energy density of the Universe at the early stage is very high, and the
Universe is in a strong-gravity regime. Therefore, the perturbation feature is
not altered from what was investigated earlier. At the attractor inflationary
stage, however, the feature is changed in the strong EiBI-gravity limit. The
correction to the scalar perturbation in this limit comes mainly via the
background matter field, while that to the tensor perturbation comes directly
from the gravity ($\kappa$) effect. The change in the value of the scalar
spectrum is little compared with that in the weak EiBI-gravity limit, or in GR.
The form of the tensor spectrum is the same with that in the weak limit, but
the value of the spectrum can be suppressed down to zero in the strong limit.
Therefore, the resulting tensor-to-scalar ratio can also be suppressed in the
same way, which makes $\varphi^2$ model in EiBI theory viable.
