<p>The theoretical research and development of wave propagation in periodic structures is the basis for studying dynamic response problems, dynamic mechanical properties of materials, medical ultrasonic problems, nondestructive testing and other problems. The isogeometric analysis (IGA), in conjunction with the high-order homogenization approach, is presented in this work for wave propagation analysis in periodic composite structures. Discretizing the microscopic characteristic function using non-uniform rational B-splines (NURBS) basis function improves the accuracy of high-order field calculations. The macro- and microscale wave equations are solved using the IGA method. The wave propagation equation is progressively expanded by using the asymptotic homogenization method based on multi-spatial scales within the isogeometric discretization framework, thereby reducing the sensitivity of the time step and the calculation time while maintaining the same level of accuracy. Several numerical examples are given to demonstrate the effectiveness of this isogeometric high-order homogenization (IGHH) model for wave propagation.</p>