Abstract: The influences of the electronic induction drag on the variation of the orbital elements of a charged satellite moving in a magnetic-field-free ionosphere are studied.The theoretical result show that the induction drag results in both the secular and periodic variation of the semi-major axis,however the eccentricity,the argument of perigee and the mean longitude of epoch exhibits no secular variation,but only periodic variation.The inclination and the ascending node remain no variation.As example,the secular effect of the induction drag on the orbital semi-major axis at a supposed satellite is calculated.It can be shown that the semi-major axis is contracted due to the induction drag,if this satellite carries many charges in an ionosphere.