A qualitative analysis has been made of a class of Holling-IV prey-predator systems with the harvest rate. By using Poincare formal series method, Poincare Bendixson ring domain theorem, Dulac theorem and branch theory, such statistics as the behavior of equilibrium point, the focus quantity of positive equilibrium point, the existence and nonexistence conditions of limit cycle can be obtained, with the main results to be verified via mathematical software.