In this paper, we are interested in the finite time blow-up behaviors of strong solutions to the compressible Navier-Stokes equations with vacuum as far field density. Via the blow-up criterion obtained by [H. Wen and C. Zhu, Adv. Math., 2013], we are able to obtain a lower bound of the blow-up rate for
$$||\nabla u||_{L^2}$$
and
$$||P||_{L^2}$$
provided that
$$\gamma >3$$
and the viscous coefficients satisfy the additional condition
$$\frac{29}{3}\mu >\lambda $$
.
