  The asymptotic behavior of the elastic scattering amplitude by the exchange
of graviton between two scalar particles at high energies and fixed momentum
transfers is reconsidered in the Logunov-Tavkhelidze equation in the linearized
gravitational theory. The corrections to the eikonal approximation in the
quasi-potential approach of relative order $1/p$ is developed with the
principal contributions at high energy. The eikonal expression of scattering
amplitude and the formal first correction are derived. The Yukawa potential is
applied to discuss the results.
