We propose a compressible associating model to describe liquid-liquid equilibria of dendritic polymer solutions. The model is based on the lattice cluster theory and the hydrogen-bonding model. We examine phase behaviors of dendritic polymer solutions on the effect of compressibility, structure and hydrogen bonding formations among polymer endgroups and solvent molecules. Our results show that the solvent-solvent hydrogen bonding and pressure dominate phase behaviors of dendritic polymer/polar solvent systems, on the other hand, a little effect on the characteristic of endgroups.