The description of a Lorentz beam is directly obtained from Maxwell's equations. Based on the vector angular spectrum representation of Maxwell's equations and the method of stationary phase, the analytical TE and TM terms of the Lorentz beam have been presented in the far field. The TE term is located at the y axis, and the TM term the x axis. The light intensity distributions of the Lorentz beam and its TE and the TM terms are depicted in the far field reference plane. The influences of the inequality of the transverse beam waists on the light intensity distributions of the Lorentz beam, its TE and TM terms are also analyzed. Moreover, the vectorial structure of the Lorentz beam is compared with that of the Gaussian beam. Due to the relatively small diffraction effect, the beam spot of the Lorentz beam is smaller than that of the Gaussian beam. This research reveals the vectorial composition of the Lorentz beam.