A JEC finite-difference time-domain (JEC-FDTD) methodology for dispersive media is extended to anisotropic magnetized plasmas. The problem which incorporates both anisotropy and frequency dispersion at the same time is solved for the electromagnetic wave propagation. The JEC-FDTD formulation for anisotropic magnetized plasmas is derived. The high efficiency and accuracy of the method are confirmed by computing the reflection and transmission through a magnetized plasma layer, with the direction of the propagation parallel to the direction of the biasing field. A comparison with frequency-domain analytic results is included.