  New results on the Deeply Virtual Compton Scattering process $\gamma^* p \to
\gamma p$ (DVCS) from H1 experiment at the $e p$ collider HERA are presented,
using data collected during the year 2004 and corresponding to an integrated
luminosity of 39.7 pb$^{-1}$. The DVCS cross section is measured as a function
of the photon virtuality, $Q^2$, the $\gamma^* p $ c.m.s. energy $W$ and
differentially in the momentum transfer squared at the proton vertex, $t$, in
the kinematic range $6.5 < Q^2 < 80 $ GeV$^2$, $30 < W < 140$ GeV and $|t| < 1$
GeV$^2$. The results are found to be in good agreement with the published H1
and ZEUS measurements and compared to NLO QCD calculations based on Generalized
Parton Distributions (GPD) and to predictions from Color Dipole Model.
