  Let $\mathrm{IG}(k, 2n+1)$ be the odd-symplectic Grassmannian. Property
$\mathcal{O}$, introduced by Galkin, Golyshev and Iritani for arbitrary
complex, Fano manifolds $X$, is a statement about the eigenvalues of the linear
operator obtained by the quantum multiplication by the anticanonical class of
$X$. We prove that property $\mathcal{O}$ holds in the case when $X=
\mathrm{IG}(k, 2n+1)$ is an odd-symplectic Grassmannian. The proof uses the
combinatorics of the recently found quantum Chevalley formula for
$\mathrm{IG}(k, 2n+1)$, together with the Perron-Frobenius theory of
nonnegative matrices.
