The effects of the finite current channel width on the current convective instability are studied both analytically and numerically. First, using a sharp-boundary field-aligned current distribution which has a finite width along the plasma density gradient, the dispersion relation is obtained analytically. Numerical results are also presented for a diffuse-boundary current velocity distribution. Applications to the high latitude ionosphere are discussed. Key words include: Plasma instability, High latitude ionosphere, Fluid instability, Finite current channel width.