Laminar natural convection heat transfer from vertical 7 × 7 rod bundle in liquid sodium was numerically analyzed to optimize the thermal–hydraulic design for the bundle geometry with equilateral square array (ESA). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The code of the parabolic hyperbolic or elliptic numerical integration code series (PHOENICS) was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 7 × 7 heated rods for diameter (D =* *0.0076 m), length (L =* *0.2 m) and L/D (=26.32) were used in this work. The surface heat fluxes for each cylinder, which was uniformly heated along the length, were equally given for a modified Rayleigh number, **(Ra**_{f,L}**)**_{ij} and **(Ra**_{f,L}**)**_{Nx×Ny,S/D}, ranging from 3.08 × 10^{4} to 4.28 × 10^{7} (q =* *1 × 10^{4}∼7 × 10^{6} W/m^{2}) in liquid temperature (T_{L} = 673.15 K). The values of ratio of the diagonal center-line distance between rods for bundle geometry to the rod diameter (S/D) for vertical 7 × 7 rod bundle were ranged from 1.8 to 6 on the bundle geometry with ESA. The spatial distribution of average Nusselt numbers for a vertical single cylinder of a rod bundle, **(Nu**_{av})_{ij}, and average Nusselt numbers for a vertical rod bundle, **(Nu**_{av}_{,B}**)**_{Nx×Ny,S/D}, were clarified. The average values of Nusselt number, **(Nu**_{av})_{ij} and **(Nu**_{av}_{,B}**)**_{Nx×Ny,S/D}, for the bundle geometry with various values of S/D were calculated to examine the effect of array size, bundle geometry, S/D, **(Ra**_{f,L}**)**_{ij} and **(Ra**_{f,L}**)**_{Nx×Ny,S/D} on heat transfer. The bundle geometry for the higher **(Nu**_{av}_{,B}**)**_{Nx×Ny,S/D} value under the condition of S/D = constant was examined. The general correlations for natural convection heat transfer from a vertical N_{x}×N_{y} rod bundle with the ESA and equilateral triangle array (ETA), including the effects of array size, **(Ra**_{f,L}**)**_{Nx×Ny,S/D} and S/D were derived. The correlations for vertical N_{x}×N_{y} rod bundles can describe the theoretical values of **(Nu**_{av}_{,B}**)**_{Nx×Ny,S/D} for each bundle geometry in the wide analytical range of S/D (=1.8–6) and the modified Rayleigh number (**(Ra**_{f,L}**)**_{Nx×Ny,S/D} = 3.08 × 10^{4} to 4.28 × 10^{7}) within −9.49 to 10.6% differences.