<p>This paper establishes the asymptotic stability of a composite wave for a damped wave equation with partially linearly degenerate flux. The global solution is shown to converge to a combination of a rarefaction wave and a viscous contact wave as time tends to infinity by employing the <i>L</i>² energy method and a refined wave interaction analysis. This is the first result on the asymptotics toward multiwave for the damped wave equation, and this asymptotic stability result does not rely on the small assumption of neither the initial perturbations nor the wave strength.</p>