The transient electromagnetic (TEM) method utilizes artificial transmitters and measures electromagnetic (EM) responses to reveal the resistivity information of the subsurface. The current waveform of transmitters has nonnegligible effects on induced fields. Therefore, 3-D TEM forward modeling algorithms need the capability of simulating arbitrary waveforms to obtain accurate responses. In time-stepping-based 3-D TEM forward modeling, the source term (ST) approach is frequently used, which employs the source current density to model the waveform variation during time-stepping. The ST approach, however, requires fine-time discretization to describe complex waveforms, which could significantly raise the computational cost. We present a robust convolution (Conv) approach that computes the convolution between the time derivative of the waveform and the step-off response to incorporate the waveform effects in 3-D TEM modeling. The Conv approach does not discretize the waveform using time steps. Hence, it is advantageous when modeling full-waveform cases. The developed algorithm is based on the finite-element (FE) method using unstructured grids and the implicit backward Euler approach. Both galvanic and inductive transmitters are incorporated. Ground and airborne TEM surveys are tested using an actual airborne TEM waveform, a full waveform of the 2(n) -sequence pseudorandom signal, and various synthetic waveforms. Accuracy is validated against the 1-D and 3-D solutions of published studies. The ST and Conv approaches are compared. Synthetic examples show that the latter approach simplifies the waveform incorporation in TEM modeling and substantially improves time-stepping efficiency without sacrificing accuracy.