The phase diagram of a protein-water system is described with a simple model with parameters for the interaction between protein molecules in the liquid and in the solid phase. The model reproduces essential features of the phase diagram, such as the (metastable) liquid-liquid immiscibility region and the triple point. The calculated phase diagram is used to analyze conditions for crystal growth. It is found that the condition for a crystallization mechanism with nucleation via a liquid-liquid phase separation as a first step corresponds closely to the favorable conditions for crystal growth reported by George and Wilson (Acta Crystallogr. 1994, D50, 361), which suggests that nucleation via liquid-liquid phase separation is the prefered mechanism for growing high quality protein crystals.