With elliptically polarized laser pulse, the nonsequential double ionization (NSDI) of argon atoms is investigated using fully classical ensemble. The results show that the yield of NSDI decreases with increase of the ellipticity, that the momentum spectrum of the correlated electron from double ionization events in the final state shows a correlated behavior along the long axis of the laser polarization plane and an anticorrelated behavior along the short axis of the laser polarization plane, and that the momentum spectrum distribution of Ar2+ ion exhibits a single-peak structure at the zero along the short axis of the laser polarization plane, which becomes broader with the increase of the ellipticity. Trajectory back analyses show that the happening of NSDI is still due to recollision, and that the delay time between the collision and the single ionization increases with ellipticity increasing, which is because that the first electron needs more trips shuttling back and forth, so that it can recollide with the parent ion under the more ellipticity.