Background: Accurate forecasts of cancer incidence, with appropriate estimates of uncertainty, are crucial for planners and policy makers to ensure resource availability and prioritize interventions. We used Bayesian age-period-cohort (APC) models to project the future incidence of cancer in Australia. Methods: Bayesian APC models were fitted to counts of cancer diagnoses in Australia from 1982 to 2016 and projected to 2031 for seven key cancer types: breast, colorectal, liver, lung, non-Hodgkin lymphoma, melanoma and stomach. Aggregate cancer data from population-based cancer registries were sourced from the Australian Institute of Health and Welfare. Results: Over the projection period, total counts for these cancer types increased on average by 3 % annually to 100 385 diagnoses in 2031, which is a 50 % increase over 2016 numbers, although there is considerable uncertainty in this estimate. Counts for each cancer type and sex increased over the projection period, whereas decreases in the age-standardized incidence rates (ASRs) were projected for stomach, colorectal and male lung cancers. Large increases in ASRs were projected for liver and female lung cancer. Increases in the percentage of colorectal cancer diagnoses among younger age groups were projected. Retrospective one-step-ahead projections indicated both the incidence and its uncertainty were successfully forecast. Conclusions: Increases in the projected incidence counts of key cancer types are in part attributable to the increasing and ageing population. The projected increases in ASRs for some cancer types should increase motivation to reduce sedentary behaviour, poor diet, overweight and undermanagement of infections. The Bayesian paradigm provides useful measures of the uncertainty associated with these projections.