As a new class of artificial elastic materials, granular crystals are mechanical structures of elastic beads arranged in contact through a lattice. One important feature of wave dynamics in granular crystals is that it highly relies on the contact mechanics, allowing for exotic wave transport properties such as rotational waves, solitary waves, slow edge waves, topological edge waves, etc. Realizing granular structures with well-predicted wave physics not only renders these new properties to mechanical systems, but provides also significant possibilities for advanced elastic wave control scenarios. Here, we theoretically and experimentally study the linear wave dynamics in one-dimensional (1D) zigzag granular chains constructed with macroscopic spherical stainless steel/tungsten beads. A spring–mass model including normal, shear and bending mechanical couplings between beads is proposed to characterize the wave dynamics in the chain, which turns out to exhibit remarkable agreement with the experimental measurements. Our work confirms the existence of localized translational–rotational coupled modes at the ends of granular chains, and it might motivate future studies for novel topological wave effects in granular structures.