Action potential initiation (API) is a crucial step in neural information integration and communication. A stable site of API is beneficial for neural coding. A specialized band with a high density of sodium channels in the axon initial segment has been proved as the primary site of API. In this paper we investigate the role of a dense sodium-channel band in the threshold and the location of API of a neuron with a multicompartment model. It is shown that the threshold of the injected current for API is enhanced by a farther distance between the stimulated site and the band and lowered by an increase of the sodium-channel density and the bandwidth. There exists an optimal location of the dense sodium-channel band, which enables the lowest threshold for API. In the case of an excitable dendrite, the site of API shifts from the band to the stimulated dendritic site with increasing stimuli strength. A larger bandwidth and higher sodium-channel density elevate the stability of the sodium-channel band as the site of API and an optimal band position enables the highest stability.