  In general relativistic framework of the large scale structure formation
theory in the universe, we investigate the relation between density contrast
and peculiar velocity in the Newtonian gauge. According to the gauge-invariant
property of the energy-momentum tensor in the Newtonian gauge, we consider the
perturbation of velocity in the energy-momentum tensor behaves as the Newtonian
peculiar velocity. It is shown that in the relativistic framework, the relation
between peculiar velocity and density contrast has an extra correction term
with respect to the Newtonian Peebles formula which in small scales, can be
ignorable . The relativistic correction of peculiar velocity for the structures
with the extension of few hundred mega parsec is about few percent which is
smaller than the accuracy of the recent observations for measuring peculiar
velocity. The peculiar velocity in the general relativistic framework also
changes the contribution of Doppler effect on the anisotropy of CMB.
