This paper investigates the output feedback security control problem of switched nonlinear systems (SNSs) against denial-of-service (DoS) attacks. A novel switched observer-based neural network (NN) adaptive control algorithm is established, which guarantees that all the signals in the closed-loop system remain bounded. Note that when a DoS attacker is active in the Sensor-Controller channel, the controller cannot acquire accurate information, which leads to the standard backstepping technique not being workable. A set of NN adaptive switching-like observers is designed to tackle the obstacle for each subsystem. Further, by combining the proposed observer with the backstepping technique, an NN adaptive controller is constructed and the dynamic surface control method is borrowed to surmount the complexity explosion phenomenon. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control algorithm.