In this paper, adaptive neural network control is investigated for a general class of strict-feedback systems using "ISS-modular" approach. The closed-loop system consists of two interconnected subsystems: the state error subsystem and the weight estimation subsystem. First, a neural controller is designed to achieve ISS for the state error subsystem with respect to the neural weight estimation errors. Then, a neural weight estimator is designed to achieve ISS for the weight estimation subsystem with respect to the system state errors. Finally, the stability of the entire closed-loop system is guaranteed by the small-gain theorem. The "ISS-modular" approach avoids the construction of an overall Lyapunov function for the closed-loop system, and overcomes the controller singularity problem completely. The simulation studies demonstrate the effectiveness of the proposed control method.