Landings from fisheries are often underreported, that is, the true landings are greater than those reported. Despite this bias, reported landings are widely used in fish stock assessments, and this might lead to overoptimistic exploitation strategies. We construct a statistical stock assessment model that accounts for underreported landings using the theory of censoring with sequential population analysis (SPA). The new model is developed and implemented specifically for the cod stock ( Gadus morhua ) from the southern Gulf of St. Lawrence (Canada). This stock is known to have unreported overfishing during 1985–1992. We show in simulations that for this stock, the new censored model can correctly detect the problematic landings. These corrections are nearly insensitive to subjective boundaries placed on real catches and robust to modifications imposed in the simulation of landings. However, when surveys are too noisy, the new SPA for censored catches can result in increased uncertainty in parameters used for management such as spawning stock biomass and age-structured stock size.