Electrical nerve stimulation using extracellular electrodes is widely performed in clinical medicine as well as basic medical science. It has been reported that selective recruitment of nerve fibers on the basis of the distance between the electrode and the axon is possible without moving the electrode and only by modifying the waveform of electrical stimulation. However, computer simulations have not reproduced the complete nature of the distance-selectivity of the stimulus owing to the difficulty in numerical analysis. In this paper, we propose a minor modification to the myelinated axon model to overcome this difficulty. We confirm that this modification improves the numerical stability of the simulation and enables us to obtain the spatio-temporal dynamics of axons, including the electrode-to-axon distance-dependency. In addition, we propose a novel stimulation method using a down-staircase waveform for distance-selective nerve recruitment. Simulations confirm that the method works well. We show the spatial distribution of axons activated by the down-staircase stimulation, which would be helpful to determine the stimulation parameters for distance-selective nerve recruitment.