To improve the performance of intercepting a target with different maneuvering modes and changing the mode suddenly during the interception, a new adaptive control algorithm for the IGC (Integrated Guidance and Control) system is proposed, using the global terminal sliding mode control method and a DNN (Deep Neural Network). Firstly, the missile-target problem is formulated and a new strict-feedback nonlinear IGC model with mismatched uncertainties is established. Secondly, the paper divides the IGC system into four subsystems, including a guidance subsystem, overload subsystem, attitude subsystem and the deep neural network subsystem. To transform the control signal between each subsystem and avoid the “differential explosion” problem, the paper defines the SOF (Second Order Filter). Thirdly, in combination with a deep neural network, a new modified global terminal sliding mode surface and the adaptive control law are designed. At last, using the Lyapunov theory, the stability of the IGC system is analyzed. Finally, to illustrate the effectiveness of the proposed algorithm, several simulation cases are given. The simulation results show the superiority of the proposed algorithm in adapting different maneuvering modes during the whole interception, improving the control performance and having a high interception accuracy.