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Abstract This manuscript presents a spatial–temporal nonlocal homogenization model for transient anti-plane shear wave propagation in viscoelastic composites. The proposed model is formulated through asymptotic homogenization with higher order corrections incorporated to extend the applicability of the homogenization theory to shorter wavelength regime. A nonlocal homogenization model in the form of a fourth order PDE is consistently derived with all model parameters directly computed from the microstructure equilibrium. A reduced order model in the form of a second order PDE is then proposed for efficient transient wave propagation analysis. The reduced model retains the dispersive character of the original nonlocal model through the effective stiffness tensor. Transient shear wave propagation in two-dimensional domain with periodic elastic and viscoelastic microstructures is investigated and the proposed models were verified against direct numerical simulations. The spatial–temporal nonlocal homogenization model is shown to accurately capture shear wave dispersion in the first pass band and attenuation within the first stop band. [ABSTRACT FROM AUTHOR]