In this paper, we derive new results for backstepping controller design for the anti-synchronization ofArneodo chaotic system (1980). Backstepping control is a recursive procedure that combines the choice ofa Lyapunov function with the design of a feedback controller. In anti-synchronization of chaotic systems,the states of the synchronized systems have the same absolute values, but opposite signs. First, we derivean active backstepping controller for the anti-synchronization of identical Arneodo chaotic systems. Next,we derive an adaptive backstepping controller for the anti-synchronization of identical Arneodo chaoticsystem, when the system parameters are unknown. The anti-synchronization results for Arneodo chaoticsystems have been proved using Lyapunov stability theory. Numerical simulations have been shown toillustrate the backstepping controllers derived in this paper for Arneodo chaotic system.