A three-dimensional slow-wave finite-element time domain algorithm is presented for the first time. Due to the slow-wave approach the carrier is removed from the field and the envelope is solved instead. This feature permits longer steps in time than when the carrier is included. A Newmark scheme, which is unconditionally stable and second order accurate, in conjunction with tetrahedrons edge-elements and absorbing boundary conditions (ABC) were adopted. Numerical results validate the present algorithm.