Abstract Fertility projections inform population projections and are used to plan for the future provision of vital services such as maternity care and schooling. Existing fertility forecasting models tend to use aggregate births data indexed by age and time alone, thereby neglecting to include information about parity, that is, the number of previous live-born children. This omission risks ignoring a crucial mechanism of fertility dynamics. We propose a Bayesian parity-specific fertility projection model to complete cohort fertility, within a generalized additive model framework. The use of such models enables a smooth age‒cohort rate surface to be estimated for each parity simultaneously. We constrain our model using aggregate data and additionally introduce random walk priors on completed family size and parity progression ratios, which are summary fertility measures known to change relatively slowly over time. Using Hamiltonian Monte Carlo methods and data from the Human Fertility Database, we fit our model to 16 countries. We compare our forecasts with the best-performing existing models to quantify the impact of including the parity dimension on predictive accuracy. Our findings indicate that a parity-specific approach could lead to more plausible and reliable fertility projections, aiding government planners in their decision-making and enabling more tailored policy solutions.