Clinical trials have demonstrated that kilohertz-frequency transcutaneous spinal cord stimulation (TSCS) can be used to facilitate the recovery of sensory-motor function for patients with spinal cord injury, whereas the neural mechanism of TSCS is still undetermined so that the choice of stimulation parameters is largely dependent on the clinical experience. In this paper, a finite element model of human percutaneous spinal cord stimulation was used to calculate the electric field distribution of human spinal cord segments T12 to L2, whereas the activation thresholds of spinal fibers were determined by using a double-cable neuron model. Then the variation of activation thresholds was obtained by varying the carrier waveform, the interphase delay, the modulating frequency, and the modulating pulse width. Compared with the sinusoidal carrier, the usage of square carrier could significantly reduce the activation threshold of dorsal root (DR) fibers. Moreover, the variation of activation thresholds was no more than 1 V due to the varied modulating frequency and decreases with the increased modulating pulse width. For a square carrier at 10 kHz modulated by rectangular pulse with the frequency of 50 Hz and the pulse width of 1 ms, the lowest activation thresholds of DR fibers and dorsal column fibers were 27.6 V and 55.8 V, respectively. An interphase delay of 5 μs was able to reduce the activation thresholds of the DR fibers to 20.1 V. The simulation results can lay a theoretical foundation on the selection of TSCS parameters in clinical trials.