The problem of fault propagation which exists in the deeply integrated GNSS (Global Navigation Satellite System)/INS (Inertial Navigation System) system makes it difficult to identify faults. Once a fault occurs, system performance will be degraded due to the inability to identify and isolate the fault accurately. After analyzing the causes of fault propagation and the difficulty of fault identification, maintaining correct navigation solution is found to be the key to prevent fault propagation from occurring. In order to solve the problem, a novel robust algorithm based on convolutional neural network (CNN) is proposed. The optimal expansion factor of the robust algorithm is obtained adaptively by utilizing CNN, thus the adverse effect of fault on navigation solution can be reduced as much as possible. At last, the fault identification ability is verified by two types of experiments: artificial fault injection and outdoor occlusion. Experiment results show that the proposed robust algorithm which can successfully suppress the fault propagation is an effective solution. The accuracy of fault identification is increased by more than 20% compared with that before improvement, and the robustness of deep GNSS/INS integration is also improved.