In this paper, we consider the one-dimensional compressible
Navier-Stokes equations for isentropic flow connecting to vacuum
state with a continuous density when viscosity coefficient depends
on the density. Precisely, the viscosity coefficient $\mu$ is
proportional to $\rho^\theta$ and $0<\theta<1/2$, where $\rho$ is
the density. The global existence of weak solutions is proved.