A new numerical scheme for electromagnetic wave tracing is presented in place of the standard ray-tracing method in studies of electron cyclotron resonance heating. The new method solves the full-wave Maxwell equations, and can take into account wave diffraction, mode conversion (or, cross-polarization scattering), and wave tunneling across an evanescent region between resonance and cutoff layers, in addition to estimating power absorption due to wave-particle resonances. The simulations of electromagnetic wave tunneling are demonstrated. The power absorption rate in electron cyclotron resonance heating is also compared with that by the ray-tracing method.