I am a beginner of this field. As we know, we can use Pseudo-compressibility idea for continuity equation in the incompressibility flow instead of a pressure-correction equation, then What's the advantage of Pseudo-compressiblity? Can you give me some words or show some papers? thank you in advance.

There are two classical approaches to solve incopressible flows: the one using pressure correction idea and the one using pseudo-compressibility idea. The choice between the first or the latter is essentially depends on personal taste, because both work well. Anyway, I think that pseudo-compressibility is used because it's easily implemented from previously existing codes for compressible flows. So, if you have a time marching code for compressible flows, the best choice, in my opinion, is the pseudo-compressibility approach. Look for "Chorin time marching" on the net to find some papers on the subject.