Iron phosphate glasses are promising nuclear waste forms while more detailed understanding of their structures and structure-property relations are still needed to better design waste glass compositions. In this work we report studies of three series of sodium iron phosphate (NFP) glasses: 60P2O5-(40-x)Fe2O3-xNa2O (x = 0→40), (100–2x)P2O5-xFe2O3-xNa2O (x = 5→17.5) and one with different iron redox ratio, to understand the composition as well as the iron redox effects on the structure and properties of these glasses using molecular dynamics simulations with effective two-body and three-body potentials. Structural analyses, including pair distribution function, bond angle distribution, Qn distribution, and polyhedral connectivity, were performed to obtain in-depth information on short-range and medium-range structural features. The P-O pair distributions showed a first peak splitting with phosphorus-bridging and non-bridging oxygen contributions. This and the average P-O and other cation-oxygen bond distances are in excellent agreement with experiments. The coordination number of P5+ remained four while that of Fe3+ increased from 4.30 to 4.72 with decreasing Fe/Na ratio. Polyhedral linkage analysis showed [PO4] units linked with [PO4] and [FeOx] through corner-sharing while the [PO4]-[FeOx] linkages become dominant for compositions with Fe2O3 larger than 15 mol%. The effect of iron redox ratio on the structure of NFP glasses was also studied and it was found that bond lengths and coordination numbers were not strongly affected, while the reduction of iron introduced higher network distortions, as evident by O-P-O bond angle and Qn distribution. The glass transition temperature (Tg) showed a monotonic increase with Fe2O3 in the first series, in good agreement with experiments, while those of the second series showed a maximum at P2O5 = 82 mol%. Calculated elastic moduli were found to increase with Fe2O3 in the first glass series, which was be explained by the increase of network connectivity, while those of the second series decrease with Fe2O3 due to decrease of P2O5.