Abstract: We present E-H time-domain finite-element method using hierarchical high-order vector basis functions. Electric fields and magnetic fields are computed together and Crank-Nicolson difference scheme is implemented to obtain an unconditionally stable algorithm. Meanwhile, perfectly matched layers are used for truncation of unbounded regions. Three-dimensional cavity and waveguide structures are simulated. It shows that accuracy is improved by E-H TDFEM method with higher-order basis functions.