This paper presents a novel approach for modeling infinite media, called Hybrid (different time integrators) Asynchronous (different time steps) Kosloff Absorbing Layers with Increasing Damping (HA-Kosloff ALID). By using strong forms of wave propagation in Kosloff media, its design equation is derived as well as optimal conditions between physical and absorbing domains. Explicit/Implicit co-simulation is adopted to reduce computation time. Examples of semi-infinite bar and Lamb’s test are implemented to illustrate the efficiency of our approach in terms of accuracy and CPU time, in comparison to Rayleigh ALID and PML. It turns out to be efficient and convenient for modeling unbounded domain.