Large-Eddy Simulation (LES) is potentially a powerful tool to provide enhanced understanding of the fundamental physical processes in supercritical injection, mixing and combustion. However, due to the lack of experimental data for validation, computational fluid dynamics (CFD) still plays a less important role in the initial design phase of a combustion system. The present study attempts to examine the effect of grid resolution and 3D flows on the LES of swirling liquid oxygen in a simplex swirl injector at supercritical conditions. The supercritical liquid oxygen cold flow in the inner element of an RD-0110 main injector is studied. Both axisymmetric and three-dimensional cases are considered. Results show that even with very fine grid resolution, the liquid film thickness and spreading angle still show grid dependent behaviors. In addition, the mixing rate is dramatically different for the axisymmetric and 3D results, indicating the necessity of using three-dimensional mesh to study the supercritical swirling flow. Three-dimensional flow features of liquid oxygen at realistic liquid rocket operating conditions are also presented.