  We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic
gauge function and a dilaton potential. A family of analytic solutions is
obtained by the potential reconstruction method. We then study its holographic
dual QCD model. The kinetic gauge function can be fixed by requesting the
linear Regge spectrum of mesons. We calculate the free energy to obtain the
phase diagram of the holographic QCD model and interpret our result as the
heavy quarks system by comparing the recent lattice QCD simulation. We finally
obtain the equations of state in our model.
