An integrity monitoring of integrated navigation in the presence of slowly growing errors (SGEs) is proposed. SGEs with gradual growth over time are the worst category of latent failures. Tightly coupled inertial navigation system (INS)/Global Navigation Satellite System integration is presented by taking INS errors, bias and drift of receiver clock, baro‐altitude, pseudo‐range errors and ionospheric errors into consideration. Based on the RTCA performance standards DO‐229 and DO‐384, the simplified multi‐filters solution separation is employed for fault detection and calculation of corresponding outputs. For the fault exclusion part, the authors introduce a post pseudo‐range residual and measurement averaging method that is designed to quickly and effectively address SGEs and large measurement noises. Furthermore, the authors have designed a reconstruction logic for the filters that guarantees the continuity of the civil aviation system by considering the variation of visible satellites and historical information. The simulation results demonstrate that the proposed approach satisfies the performance requirements for civil aviation of En‐route and is able to correctly exclude faults and respond quickly in the presence of different levels of SGEs and measurement noises.