In this paper, we present a full quantum description for coupling mechanism of the metamaterial. We start the derivation from quantum master equation to fit the spectrum of THz metamaterial. Therefore we can employ the quantum master equation to describe the coupling of metamaterial, such as the electromagnetically induced transparency (EIT) and bound state in the continuum (BIC). In this paper, we build up a bridge between the quantum mechanism and coupling mechanism of metamaterial, so-called quantum–classical analogies. Based on our theory, we can find the more quantum phenomenon with corresponding to the coupling phenomenon of the metamaterial.