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Topological acoustic insulators enable sound waves to transmit along the surface without backscattering, which builds a new pathway towards sound wave control. However, a large share of topological acoustic insulators are realized based on special point group symmetry and Bragg scattering mechanism. This method not only exerts a restriction on the unit cell design but also requires the lattice constant to be comparable with the wavelength. In this paper, the chiral spiral acoustic metamaterials are constructed based on an Archimedean spiral structure. This structure enjoys subwavelength characteristics and is easy to construct. Taking advantage of the chirality of the spiral structure topological phases with opposite energy flow direction can be constructed. The edge state is formed at the interface composed of the spiral units sharing different chirality, which does not depend on point group symmetry. The topological transportation on the interfaces shows strong robustness despite sharp corners verified by straight and zigzag waveguides. The topological acoustic insulator with a chiral spiral structure provides a novel strategy for small acoustic devices with robust sound transmission.