We use a Spectral-Element Method implemented on the Earth Simulator in Japan to simulate broadband seismic waves generated by various earthquakes. The spectral-element method is based on a weak formulation of the equations of motion and has both the flexibility of a finite-element method and the accuracy of a pseudospectral method. The method has been developed on a large PC cluster and optimized on the Earth Simulator. We perform numerical simulation of seismic wave propagation for a three-dimensional Earth model, which incorporates 3D variations in compressional wave velocity, shear-wave velocity and density, attenuation, anisotropy, ellipticity, topography and bathymetry, and crustal thickness. The simulations are performed on 4056 processors, which require 507 out of 640 nodes of the Earth Simulator. We use a mesh with 206 million spectral-elements, for a total of 13.8 billion global integration grid points (i.e., almost 37 billion degrees of freedom). We show examples of simulations for several large earthquakes and discuss future applications in seismological studies.