In the present article we have developed an analytical model and did a numerical simulation to study the motion of the artificial earth’s satellite. We considered a model in which a celestial body(satellite) moving under the gravitational field of an oblate body and in presence of grav-itational pull of other distant body. We begin by expressing disturbing function in terms of Legendre’s polynomial and restricted our calculations up to second-order terms. Our methodology consists of a double averaging technique over the periods of perturbed and perturbing bodies. The focus of this work is to study the effect of the oblate shape of the central body on the orbital elements of the test particle in the framework of restricted three-body problem. We compare the evolution of orbital elements graphically when the central body has an oblate shape with the case when it is a point mass and illustrate the effect of oblateness on eccentricity , inclination, and argument of pericentre. On changing the shape of the central body from point mass to oblate shape, we noticed significant changes in orbital elements of perturbed body. The double averaged model(say) in this article can be applied on other systems but we have applied it to earth’s satellite movement in the medium earth orbit(MEO) region when it is perturbed by the moon.