Initial step voltage during the interruption of short-circuit current in a fuse has an important effect on the current-limiting capability of fuse and the working security of electric equipment. The initial arc column voltage makes the main part of the step voltage. In this paper, we discovered the approximate linear relationship between current density the moment arc starts, ranging from 10 to 45 kA/mm2, and the initial arc column voltage gradient, through the analysis of interrupting experiments using sample fuses containing single stripe of silver with one constriction, pre-arcing energy and the packing density of silica sand remained the same. The above law is applied in the circumstance of the fuselink with multiple constriction in series and a further investigation of the initial step voltage influenced by the number of notch is carried out, which provides basis for small scale experiment on the series characteristics of multiple notches for high voltage.