<p>Although significant advancements have been made in understanding the physics of cytoskeletal substructures, the research on structural interactions and cross-talk between actin filaments, microtubules, and intermediate filaments is still in its infancy. Here, we report a coarse-grained hierarchical computational model based on the Langevin dynamics method to investigate the mechanical response of the composite actin-microtubule networks. It was found that strain stiffening occurred in all three types of networks: actin network, microtubule network, and actin-microtubule composite network with increasing shear deformation. We also found that the mechanical response of the actin-microtubule composite network is not a linear superposition of the actin and microtubule networks, but is synergistically regulated by spatial interactions to make the composite network exhibit rich mechanical properties. Load distribution within the actin-microtubule composite network was found to be controlled by the stiffness of the cross-linkers. We also examined the nonaffine deformation degree of the actin-microtubule composite network and its components. This work will contribute fresh sights for the advancement of biomimetic materials.</p>