  We consider the scalar perturbations of Eddington-inspired Born-Infeld
braneworld models in this paper. The dynamical equation for the physical
propagating degree of freedom $\xi(x^\mu,y)$ is achieved by using the
Arnowitt-Deser-Misner decomposition method: $F_1(y) {\partial_y^2 \xi} +
F_2(y){\partial_y \xi } + {\partial^{\mu}\partial_{\mu}}\xi=0$. We conclude
that the solution is tachyonic-free and stable under scalar perturbations for
$F_1(y)>0$ but unstable for $F_1(y)< 0$. The stability of a known analytic
domain wall solution with the warp factor given by $a(y)=
\text{sech}^{\frac{3}{{4p}}}(ky)$ is analyzed and it is shown that only the
solution for $0<p<\sqrt{8/3}$ is stable.
