As the structure of the underground space becomes increasingly complex, traditional 2-D seismoelectric methods are no longer adequate for comprehensive exploration. To achieve precise imaging of the underground space, there is an urgent need to develop 3-D full-waveform modeling techniques. In this article, we propose a 3-D time-domain finite-element method to solve the seismoelectric wavefield in saturated porous media. Since the electroosmotic feedback is very small, we can ignore the mechanical disturbance caused by the electromagnetic (EM) fields induced by seismic waves and, thereby, can decouple the electrokinetic coupling equations and separately solve the seismic and EM waves. For the simulation of seismic wavefield, we employ the explicit finite-element method and utilize a lumped mass matrix instead of a consistent mass matrix to facilitate explicit recursion. In addition, we apply the complex frequency-shifted unsplit perfectly matched layer technique to effectively handle seismic boundary conditions. Then, the velocity fields obtained by solving the poroelastic equations serve as the source term of the EM equations, and the finite-element method is used to solve the EM wavefield. Considering that the huge velocity difference exists between the EM and seismic waves, we adopt an unconditionally stable implicit method for the solution of the EM wavefield. By combining explicit and implicit recursion, the computational efficiency can be improved significantly. The accuracy of our time-domain finite-element algorithm is validated by checking our results against the analytical solutions for a half-space model. Furthermore, we conduct numerical simulations and analyses on a typical block model and a modified SEG/EAEG salt dome model.