In this paper, a class of predator-prey systems with two harvesting rates is studied, multiple limit cycles can be obtained by hopf bifurcation, and the Hopf cyclicity at the origin is $ 4 $. Multiple stable states can coexist in the predator-prey systems with two harvesting rates. Then by using Poincare-Bendixson theorem and Dulac discriminant method, existence and non-existence conditions of limit cycles are obtained.