We study nonlinear effects in step bunching in a surface diffusion field with a direct electric current. Linear stability analysis shows that the bunching instability occurs in sublimation at long wavelength if the step distance is smaller than the surface diffusion length and the drift of adatoms induced by the electric current is in the step down direction. When we take account of the nonlinear effect, the density of steps obeys the Benney equation, which shows an array of step bunches or spatiotemporal chaos. This feature is similar to the step bunching caused by the asymmetry of step kinetics except that the surface profile may change with the sign of the dispersion term.