To realize wall-modeled large-eddy simulations on Cartesian grids, a wall-boundary condition for non-body-conforming grids is developed. A slip-wall velocity boundary condition is introduced to reduce the error of the conservation law caused by the under-resolved velocity profile near the wall boundary. Corresponding to the slip velocity, the stress balance near the wall boundary is analyzed. To satisfy the stress balance, an anisotropic expression of the viscous-stress tensor is introduced that tends not to inhibit the wall-normal mixing by the turbulence. In the simulation of the flat-plate turbulent boundary layer, the result obtained by the developed wall-boundary condition shows a significant improvement from the results using the non-slip boundary condition in predicting both velocity and Reynolds shear stress profiles in the boundary layer.