Significance Intracellular transport of critical cellular components (e.g. vesicles, organelles, mRNA, chromosomes) is accomplished by myosin Va molecular motors along complicated 3D networks of actin filaments. Disruption of these transport processes leads to debilitating human disease (e.g. Griscelli syndrome), while rearrangement of the 3D actin cytoskeleton is a hallmark of malignant cancers. We found that the various modes of motion (stationary, diffusive-like, or directed) describing how teams of myosin Va transport 350-nm liposome cargos are determined by the 3D position and polarity of the actin filaments within the network that the myosin Va motors interact with. This study demonstrates that the 3D actin filament organization within the network can serve as a potent regulator of myosin Va motor-based intracellular transport.