Entropy bound for a rotating system from anti-de Sitter black holes

General geodesic equations of the motion of spinning systems around the (3+1)-dimensional and (2+1)dimensional rotating anti-de Sitter black holes an obtained. Based upon these equations, we derive the entropy bound for a rotating system from Kerr-anti-de Sitter black holes and Banados-Teitelboim-Zanelli black holes, respectively. Our result coincides with that of Hod's derived from a Kerr black hole, which shows that the entropy bound of the rotating system is neither dependent on the black hole parameters nor on spacetime dimensions. it is a universal entropy bound.