Abstract: A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving timedependent wave equations.Acoustic propagation problems in 1 + 1,2 + 1,3 + 1 dimensions with the dirichlet boundary conditions are simulated via space-time spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision and the dispersion is stable over time.With the same total number of grid nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.