In this technical note, we consider adaptive learning control problem for a class of nonlinear systems with periodic bounded disturbances. The bounds of the disturbance are unknown, and the minimum period T* of the disturbance can be written as T* = l* tau, with tau being a known constant and l* being an unknown integer. Our proposed adaptive controller consists of a learning law and two kinds of parameter tuning mechanisms: one is the conventional parameter update law, and the other is a logic-based switching mechanism which tunes in a switching manner the saturation level and the period in the learning law. It has been proved that under our proposed control all closed-loop states are bounded and asymptotic regulation is achieved.