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. It is found that for the long wavelength modes (ky d ≪1) where the nonlocal effects are most prominent, the growth rate &ggr; is proportional to ‖V¿d d/L2‖ in the collisional limit (vin ≫‖&ohgr;‖), where d is the half width of the current channel, L is the plasma density gradient scale length, V¿d is the field-aligned current velocity, vin is the ion-neutral collision frequency, and &ohgr; is the perturbation frequency. For the long wavelength modes in the inertial limit (vin ≪‖&ohgr;‖) the growth rate &ggr; scales as ‖V¿d d/L2‖&agr;, where &agr;=1/2 (2/3) for kz2/ky2 &OHgr;e/vei much less than (greater than) ‖&ohgr;‖/&OHgr;i, kz(ky) is the wave number (perpendicular) to the magnetic field, &OHgr;e(&OHgr;i) is the electron (ion) gyrofrequency, and vei is the electron-ion collision frequency. Numerical results are also presented for a diffuse boundary current velocity distribution. Applications to the high-latitude ionosphere are discussed.