Grey nurse sharks off the east coast of Australia are listed nationally as “critically endangered” under Schedule 1 of the Environmental Protection and Biodiversity Conservation Act (1999) and may number no more than 300 in New South Wales and southern Queensland waters. They are an inshore, coastal dwelling species and were severely depleted by spearfishing in the 1960s. The population has continued to decline despite protection since 1984. Their life history (long-lived to 25+ years), late maturation (6–8 years), low fecundity (maximum 2 live young biennially), specific habitat requirements, limited inshore distribution, and small population size render them particularly vulnerable to extinction. We estimated the time to quasi-extinction (years elapsed for the population to consist of ⩽50 females) for the grey nurse shark population off the east coast of Australia based on current estimates of abundance and known anthropogenic rates of mortality. Estimated minimum population size was 300 as of 2002, and minimum anthropogenic mortality assessed from recovered carcasses was 12/year of which 75% were females. We modelled time to quasi-extinction using deterministic age- and stage-classified models for worst-, likely and best-case scenarios. Population size was estimated at 300 (worst), 1000 (likely) and 3000 (best). Anthropogenic mortality was added to the model assuming either all carcasses are being recovered (best), or conservatively, that only 50% are reported (realistic). Depending on model structure, if all carcasses are being reported, quasi-extinction times for worst-, likely and best-case scenarios range from 13 to 16 years, 84–98 years and 289–324 years, respectively. If under-reporting is occurring, time to quasi-extinction ranges from 6 to 8 years, 45–53 years and 173–200 years, respectively. In all scenarios modelled the grey nurse shark population will decline if no further steps are taken to remove anthropogenic sources of mortality. Because estimates of quasi-extinction rate depend on initial population size, and sensitivity analysis revealed that population rate of change was most sensitive to changes in the survival probability of the smallest length classes, obtaining precise estimates of abundance and annual survival of young females is critical.