This paper proposes a novel method to correct numerical phase velocity errors in FDTD meshes with nonuniform step size. It enables the complete compensation of the phase velocity errors introduced by the mesh grading for one frequency and one arbitrary direction of propagation independently of the mesh grading. This permits the usage of the Total-Field-Scattered-Field formulation in connection with electrically large nonuniform FDTD meshes and allows a general reduction of the grid dispersion errors. The capabilities of the proposed method are demonstrated with the help of two examples: (1) the fields in a dielectric sphere illuminated by a plane wave are calculated and (2) a patch antenna simulation demonstrates that the uncertainty in determining its resonance frequency can be reduced by about 50%.