A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Numerical simulations for a vertical electrical dipole have been conducted to demonstrate the benefits of the proposed method. Results have been compared with those of the spherical FDTD algorithm and it is showed that numerical grid anisotropy can be reduced highly by WRG-FDTD.