We report a computational model for the assembly of HIV-1 Gag into immature viral particles at the plasma membrane. To reproduce experimental structural and kinetic properties of assembly, a process occurring on the order of minutes, a coarse-grained representation consisting of a single particle per Gag molecule is developed. The model uses information relating the functional interfaces implicated in Gag assembly, results from cryo electron-tomography, and biophysical measurements from fluorescence microscopy, such as the dynamics of Gag assembly at single virions. These experimental constraints eliminated many classes of potential interactions, and narrowed the model to a single interaction scheme with two non-equivalent interfaces acting to form Gags into a hexamer, and a third interface acting to link hexamers together. This model was able to form into a hexameric structure with correct lattice spacing and reproduced biologically relevant growth rates. We explored the effect of genomic RNA seeding punctum growth, finding that RNA may be a factor in locally concentrating Gags to initiate assembly. The simulation results infer that completion of assembly cannot be governed simply by Gag binding kinetics. However the addition of membrane curvature suggests that budding of the virion from the plasma membrane could factor into slowing incorporation of Gag at an assembly site resulting in virions of the same size and number of Gag molecules independent of Gag concentration or the time taken to complete assembly. To corroborate the results of our simulation model, we developed an analytic model for Gag assembly finding good agreement with the simulation results.