  We obtain a new expression of the Friedmann-Robertson-Walker metric, which is
an analogue of a static chart of the de Sitter space-time. The reduced metric
contains two functions, $M(T,R)$ and $\Psi(T,R)$, which are interpreted as,
respectively, the mass function and the gravitational potential. We find that,
near the coordinate origin, the reduced metric can be approximated in a static
form and that the approximated metric function, $\Psi(R)$, satisfies the
Poisson equation. Moreover, when the model parameters of the
Friedmann-Robertson-Walker metric are suitably chosen, the approximated metric
coincides with exact solutions of the Einstein equation with the perfect fluid
matter. We then solve the radial geodesics on the approximated space-time to
obtain the distance-redshift relation of geodesic sources observed by the
comoving observer at the origin. We find that the redshift is expressed in
terms of a peculiar velocity of the source and the metric function, $\Psi(R)$,
evaluated at the source position, and one may think that this is a new
interpretation of {\it Gentry's new redshift interpretation}.
