A three-dimensional finite-element time domain scheme based on the envelope approach is presented for the first time. In this approach the fast wave component or carrier is removed from the field and the envelope is solved instead. This strategy permits longer time steps than when the carrier is included, for the same spatial refinement. The unconditionally stable and second-order accurate Newmark scheme, in conjunction with tetrahedron edge elements and absorbing boundary condition (ABC) method was adopted. Key numerical results validate and show the efficiency and usefulness of the present algorithm.