A numerical study is carried out to investigate the mixing and atomization characteristics of liquid oxygen/kerosene swirl coaxial injectors at supercritical conditions. The numerical scheme is based on full-conservation laws and accommodates real-fluid thermodynamics and transport theories over the entire range of fluid states. Turbulence closure is achieved using large eddy simulation. A grid independence study was first conducted to ensure accurate numerical resolution and underlying flow physics. The mixing characteristics and flow dynamics were discussed in depth. Various geometric parameters, including recess region, post thickness, and kerosene annulus width, are examined to explore their influence on mixing efficiency and flow dynamics. The recess region enhances the interaction of liquid oxygen and kerosene and improves the mixing efficiency. A larger post thickness or larger annulus width imposes a higher spreading angle of the liquid-oxygen film and intercepts the kerosene film in a broader area, thereby facilitating mixing in the recess region. But the flow structures in the recess region are complicated and the mixture ratio in the vicinity of the injector post is close to stoichiometric, which leads to the potential overheating in case of combustion. An appropriate selection of the post thickness, recess length, and annulus width must be carefully made for optimum injector performance. The present study provides important information for injector design and underlying flow physics.