To ensure navigation integrity for safety-critical applications, this paper proposes an efficient Fault Detection and Exclusion (FDE) scheme for tightly coupled navigation system of Global Navigation Satellite Systems (GNSS) and Inertial Navigation System (INS). Special emphasis is placed on the potential faults in the Kalman Filter state prediction step (defined as “filter fault”), which could be caused by the undetected faults occurring previously or the Inertial Measurement Unit (IMU) failures. The integration model is derived first to capture the features and impacts of GNSS faults and filter fault. To accommodate various fault conditions, two independent detectors, which are respectively designated for GNSS fault and filter fault, are rigorously established based on hypothesis-test methods. Following a detection event, the newly-designed exclusion function enables (a) identifying and removing the faulty measurements and (b) eliminating the effect of filter fault through filter recovery. Moreover, we also attempt to avoid wrong exclusion events by analyzing the underlying causes and optimizing the decision strategy for GNSS fault exclusion accordingly. The FDE scheme is validated through multiple simulations, where high efficiency and effectiveness have been achieved in various fault scenarios.