This paper concerns with the number and
distribution of limit cycles of a perturbed cubic Hamiltonian
system which has 5 centers and 4 saddle points. The stability
analysis and bifurcation methods of differential equations are
applied to study the homoclinic loop bifurcation under
$Z_2$-equivariant cubic perturbation. It is proved that the
perturbed system can have 11 limit cycles with two different
distributions, one of which is already known, the other is new.