Abstract: Using the method of qualitative analysis it investigates the number and distribution of limit cycles for a cubic Hamiltonian system with nine different nine-order perturbed terms.It shows that these perturbed systems have the same distribution of limit cycles.Furthermore,these systems have 14 limit cycles for some parameters. The accurate location of each limit cycle is given by numerical exploration.Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles.This is useful for studying limit cycles of perturbed systems.