  In this paper, we construct a class of global large solution to the
three-dimensional Navier-Stokes equations with the Coriolis force in critical
Fourier-Besov space $\dot{FB}^{2-\frac{3}{p}}_{p,r}(\mathbb{R}^3)$. In fact,
our choice of special initial data $u_0$ can be arbitrarily large in
$\dot{FB}^{s}_{p,r}(\mathbb{R}^3)$ for any $s\in\mathbb{R}$ and $1\leq p,r\leq
\infty$.
