To show how to achieve the extraordinary transmission of one-dimensional metallic gratings with sub-wavelenghth slits, the transmission distribution of transverse electric (TE) wave through one-dimensional metallic gratings with sub-wavelenghth slits with a dielectric substance applied on it in different ways has been simulated by the finite-difference time-domain method. The relations between the refractive index of dielectric and the transmission efficiency is elicited from simulation, which show that the extraordinary transmission can be produced at several special wavelengths. Then, a new theory named the guided-mode-like resonance theory is put forward based on the guided-mode resonance theory, which is well suited for the extraordinary transmission under the TE-polarized wave excitation, and it is concluded that the guided-mode-like resonance is the main reason for the extraordinary transmission of TE-polarized wave. Thus, the new theory can explain the problems which cant be explained by the traditional theory. In a word, the guided-mode like resonance theory reveals the physical nature of the extraordinary transmission phenomenon which provides a theoretical basis for the further study of the extraordinary transmission phenomenon.