In this paper the effect of gravitational radiation damping on the variation of the orbital elements of binary system is studied using the method of perturbation. This effect results in both the secular and periodic variation of the semimajor axis and the eccentricity, however, the longitude of periastron exhibits no secular variation, but only periodic variation In addition, the deduced expression is applied to calculate the variation of secular and periodic terms of the orbital elements of binary system, Y cyg, PSR 1913 + 16 and PSR 2303 + 24, and the obtained results are discussed and compared with the relativistic effects.