Relationship between field-aligned current density and potential difference of current-driven double layer is studied by one-dimensional numerical simulations. The simulation domain is assumed to be located at a high altitude (>several earth radii) along the auroral field lines. The plasma sheet boundary supplies a plasma with number density n. Only the electrons injected from this boundary are allowed to have a drift velocity vd, which carries an upward field-aligned current. The double layer potential is spontaneously produced by the space charge self-consistently developed inside the simulation domain. For a given drift velocity vd, the relationship between the total current density J and the potential difference ϕ0 across the simulation domain is obtained by changing the number density n of the injection current. The results show that the double layer starts to be formed when the current density significantly exceeds the thermal current density of the ambient electrons and the potential difference ϕ0 increases with increasing current density J. It is also shown that at a given number density of the injection current the potential difference ϕ0 increases with increasing drift velocity vd.