  We propose a hybrid parameterization of a quasiparticle equation of state,
where a critical point is implemented phenomenologically. In this approach, a
quasiparticle model with finite chemical potential is used to describe the
quark-gluon plasma phase by fitting to the lattice quantum chromodynamics data
at high temperature. On the other hand, the hadronic resonance gas model with
excluded volume correction is employed for the hadronic phase. An interpolation
scheme is implemented so that the phase transition is a smooth crossover when
the chemical potential is smaller than a critical value, or otherwise
approximately of first order according to Ehrenfest's classification. Also, the
thermodynamic consistency is guaranteed for the equation of state related to
both the quasiparticle model and the implementation of the critical point.
