Nonsequential Double Ionization (NSDI) is a basic physical process of the interactions of strong laser fields with matter. The two electrons involved in NSDI are highly correlated, which provides a simple and effective method for understanding the electron correlation. In the past three decades, the ionization mechanism of NSDI has been studied extensively. Based on the two-hump structure of ion momentum distributions and the disappearance of the“knee”structure in the circularly polarized laser fields, the recollision model has become a very suitable ionization mechanism. The mechanism is divided into three steps. Step 1: An electron in the atom or molecule is ionized in the laser field; step 2: The ionized electron is accelerated in the laser field. When the direction of the laser field changes, the ionized electron may be pulled back and recollide with the parent ion; step 3: After recollision, the returning electron can transfer a part of the energy to the bound electron, and finally, both electrons ionize immediately or with a time delay. In linearly polarized pulses, electrons are driven by electric field force only in one direction. The returning probability is relatively high and thus results in a high double ionization yield. Therefore, early studies mainly focus on linear polarization. In this case, the control of electron dynamics is confined to one dimension. To manipulate electrons in two-dimensional space, recently, much attention has been focused on the combined electric field composed of two pulses, such as the Counter-rotating Two-color Circularly Polarized (CTCP) laser fields. By changing laser parameters, the CTCP fields can control double ionization yield, electron returning direction and returning energy. However, the waveform of the combined electric field formed by the two-colour circularly polarized pulses has multiple-fold symmetry, and the ionized electrons can return from multiple directions. If two elliptically polarized pulses are used to form a combined electric field, the multiple-fold symmetry of the electric field waveform can be broken. Thus the final emission direction of electrons and returning direction will be asymmetrical in Counter-rotating Two-color Elliptically Polarized (CTEP) fields. The ultrafast dynamics in NSDI by CTEP fields is more rich and more interesting. This paper, systematically studies the ellipticity dependence of Nonsequential Double Ionization (NSDI) of Ar atoms in CTEP fields using a three-dimensional classical ensemble model. Numerical results show that NSDI probability increases with the ellipticity of an 800-nm pulse and decreases with the ellipticity of a 1 600 nm pulse. It is because when the ellipticity of the 1 600 nm pulse is fixed, the electron returning probability and recollision energy increase with the increase of the ellipticity of the 800 nm pulse. When the ellipticity of the 800 nm pulse is fixed, the electron returning probability and recollision energy decrease with the increase of the ellipticity of the 1 600 nm pulse. Moreover, when the ellipticity of the 1 600 nm pulse is 0.3, with the ellipticity of the 1 600 nm pulse increasing the ion momentum distribution moves from the left to the right. As the ellipticities of 1 600 nm and 800 nm pulses increase, the ion momentum distribution gradually expands in the y direction and finally forms a two-layer structure distributed on both sides of the x axis.