The octupole excitations of β-stable nucleus 20882 Pb126, a neutron skin nucleus 6200Ca40 and a drip-line nucleus 288O20 are studied by using the self-consistent Hartree-Fock calculation plus the random phase approximation (RPA) with Skyrme interaction. The lowest isoscalar (IS) excitation below threshold for nuclei 20882 Pb126 and 6020Ca40, and the IS and isovector (Ⅳ) giant resonances of nuclei 20882 Pb126, 6020Ca40 and 288 O20 can be well described by collective model. For skin nucleus 2600Ca40 and drip-line nucleus 288 O20, the low-lying unperturbed neutron octupole strength (△N ＝ 1) of transitions to non-resonant states are nearly unaffected and the transitions to bound states are absorbed into collective states by taking into account the RPA correlation.