We theoretically investigate the effect of a single finite-size attractive impurity on the electron transport of a semiconductor quantum wire under the influence of a terahertz electromagnetic field illumination. In the freeparticle framework, the time-dependent electronic states are obtained by introducing an unitary transformation,and the electronic transmission of the system is obtained by using the scattering matrix approach. In the case of the field frequency resonant with the lateral energy spacing of the two lowest levels, a step-like structure for the transmission probability versus the total electron energy is predicted. Furthermore, due to the interplay between the single impurity and the applied field, the transmission probability curve in the non-resonant case shows a structure of a resonance dip on the interference patte background with certain parameters of the impurity.