Bioinks with rapid photocrosslinking are key to high-fidelity and fast light-based biofabrication. Use of visible-light can avoid unwanted mutations in the cells, however, requires Type-II photoinitiators which makes the photopolymerization highly complex. In order to predict the result of visible light bioprinting and direct the scaffold design, a better understanding of this complex process is ... [Show full abstract] needed. To address this requirement, we present a detailed numerical model of photo-pattern projection photopolymerization for SLA biofabrication. In the model, a photocrosslinkable bioink is used which consists of gelatin methacryloyl (GelMA) macromer and a visible-light photoinitiator with three-components. This model was able to emulate the underlying photoinitiation, quenching and polymerization reaction kinetics using the relevant experimental conditions. The expected crosslinked hydrogel structures expected under given photocrosslinking conditions could also be simulated and highlighted several printing inaccuracies. These inaccuracies emerged from the diffusive transport of chemical species and the dynamics of the polymerization and quenching reactions in the bioink. The influence of oxygen in inhibiting the photopolymerization was also elucidated through the processes occurring at various points in the bioink. Next, we introduced variations in the photo-pattern design and examined their effect on the hydrogel formation with time. Applying a photo-pattern projection in a pulsed manner demonstrated that bioprinting inaccuracies can be suppressed to obtain uniformly crosslinked hydrogel but at the expense of bioprinting speed. In summary, the photopolymerization model described here could prove to be a valuable tool in predicting the hydrogel formation from bioinks as well as designing scaffolds and planning out the SLA bioprinting process.