A new type of metamaterial element is proposed to possess time-dependent effective inertial mass, and proved to be valid for the design of the space-time lattice metamaterial that enables non-reciprocal wave propagation. The cell structure is a three-body dynamic system, consisting of a primary body plus two additional bodies that move along the circular orbit. The translational momentum contributed by the orbiting bodies varies periodically depending on their temporal phases, accounting for the time-driven inertial mass observed macroscopically, as verified by the rigorous theoretical derivation. Based on the time-varying mass element, we present the design of the lattice metamaterials with inertial mass that varies periodically in both space and time. Non-reciprocal wave phenomena due to the wave-like modulation of mass are demonstrated by use of the Bloch-based method and the effective-mass representation. The influence of the modulating frequency and amplitude on the asymmetric bandgap is analyzed. The proposed time-varying metamaterial with the non-reciprocal wave behavior is expected to open a new avenue towards unprecedented control over waves and vibrations. (C) 2018 Elsevier Ltd. All rights reserved.