  We construct the equation of state (EoS) of QCD based on the finite chemical
potential information from the functional QCD approaches, with the assistance
of the lattice QCD EoS. The obtained EoS is consistent with the up-to-date
estimations of the QCD phase diagram, including a phase transition temperature
at zero chemical potential of $T=155$ MeV, the curvature of the transition line
$\kappa=0.016$ and also a critical end point at $(T,\mu_B)=(118, 600)$ MeV. In
specific, the phase diagram mapping is achieved by incorporating the order
parameters into the EoS, namely the dynamical quark mass for the chiral phase
transition together with the Polyakov loop parameter for the deconfinement
phase transition. We also implement the EoS in hydrodynamic simulations to
compute the particle yields, ratios and collective flow, and find that our
obtained EoS agrees well with the commonly used one based on the combination of
lattice QCD simulation and hadron resonance gas model.
