Slow light technique has significant potential applications in many contemporary photonic device developments for integrated all-optical circuit, such as buffers, regenerators, switches and interferometers. In this paper, we present an efficient coupling mechanism of an electromagnetically induced transparency like (EIT-like) effect in an all-dielectric nano-metamaterial. This EIT-like effect is generated by destructive interference between a radiative Fabry-Perot (FP) mode and a dark waveguide (WG) mode, which is based on a combined structure of a dielectric grating and multilayer films. The dark WG mode is excited by guided mode of dielectric grating instead of radiative FP mode. In analogy to the molecular transition process, the FP mode, guided mode and WG mode are denoted by excited states of |1〉, |2〉 and |3〉. The two coupling pathways of the EIT-like effect in our metamaterial are |0〉 → |1〉 and |0〉 → |2〉 → |3〉 → |1〉, where |0〉 is the ground state. The simulated resonant wavelength of WG mode is consistent with theoretical result. We further confirm this EIT-like effect through a two-oscillator coupling analysis. We achieve a group refractive index of 913.6 by adjusting these two modes coupling of the EIT-like effect, which is useful for developing slow light device. This work provides a valuable solution to realize electromagnetically induced transparency in all-dielectric nanomaterial.