  In this paper, we derive the large-time profile of solutions to the Cauchy
problem of a hyperbolic-parabolic system modeling the vasculogenesis in $\R^3$.
When the initial data are prescribed in the vicinity of a constant ground
state, by constructing a time-frequency Lyapunov functional and employing the
Fourier energy method and spectral analysis, we show that solution of the
Cauchy problem tend time-asymptotically to linear diffusion waves around the
constant ground state with algebraic decaying rates under certain conditions on
the density-dependent pressure function.
