We present the liquid-liquid equilibria of a homogeneous dendrimer solution using a lattice cluster theory and a specific interaction model. We examined the phase behavior of dendrimer solutions by varying the dendrimer generation number, the number of bonds between two consecutive branch points along a chain, and the strength of specific interaction among end-groups of dendrimer and solvent molecules. There was only a slight change in the liquid-liquid coexistence curve of dendrimer solutions for various generation numbers. The critical temperature increases with decreasing generation number and increasing separator length. Our results show that the coexistence curve shows a great dependence on specific interactions and structure factors.