The numerical simulation of turbulent supercritical water flows is presented. In the present method, the supercritical-fluids simulator is coupled with the building-cube method because of its simplicity and efficiency, and a meshless method is implemented as a wall boundary treatment because of its flexibility and adaptability. The implementation of the SST turbulence model has been accomplished to deal with the turbulent supercritical-fluid flows. The supercritical water jet submerged in a subcritical water environment is simulated, which is a typical process of supercritical-fluid flows in the hydrothermal spallation drilling application. First, turbulence model implementation verification is proposed with the classical case of zero pressure gradient flat plate. Then, the effects of temperature and pressure on the behavior of the supercritical water jets are investigated.