A finite difference time domain （FDTD） method is used to numerically study the power absorption of broadband terahertz （0.1 - 1.5 THz） electromagnetic waves in a partially ionized uniform plasma layer under low pressure and atmosphere discharge conditions. The power absorption spectra are calculated numerically and the numerical results are in accordance with the analytic results. Meanwhile, the effects on the power absorption are calculated with different applied magnetic fields, collision frequencies and electron number densities, which depend strongly on those parameters. Under the dense strongly magnetized plasma conditions, the absorption gaps appear in the range of 0.3 - 0.36 THz, and are enlarged with the increasing electron number density.
