  This paper is concerned with a non-isentropic compressible
Navier-Stokes/Allen-Cahn system with phase variable dependent viscosity
$\eta(\chi)=\chi^\alpha$ and temperature dependent heat-conductivity
$\kappa(\theta)=\theta^\beta$. We show the global existence of strong solutions
under some assumptions on growth exponent $\alpha$ and initial data. It is
worth noting that the initial data could be large if $\alpha\ge0$ is small, and
the growth exponent $\beta>0$ can be arbitrary large.
