In this work, a concept of constructing inertant seismic metamaterials for Rayleigh wave attenuation using inerter-based vibration absorbers (IDVAs) is proposed. The dynamic behaviors of the vibration absorbers are controlled by an inertant mechanical network, while three typical oscillator configurations are considered in the design of the proposed inertant seismic metamaterial. An expanded effective medium method is developed to obtain the dispersion of Rayleigh waves, which is separated into three branches by two broad Rayleigh wave band gaps at low frequencies. The influences of the inertance-to-mass ratio as well as the stiffness ratio on the Rayleigh wave propagation are thoroughly discussed. The results show that the multiple-resonance IDVAs can efficiently open low frequency band gaps of the inertant seismic metamaterial without having to increase the mass of the resonators. Band gaps of the low-frequency Rayleigh waves can be further merged to form an extra wide one by adding dissipative mechanisms, which further enhance the attenuation of the Rayleigh waves. Specifically, by analyzing the corresponding displacement fields, it is observed that the seismic energy propagating as Rayleigh surface waves is converted to that propagating as bulk waves not concentrated to the surface, which offers a protected area behind the inertant seismic metamaterials for the facilities located at the surface of the half space. This work provides a new approach for seismic vibration isolations utilizing inertant seismic metamaterials that can be applied in protecting large infrastructures or civil engineering architectures.