  We consider an extension of the standard model in which a singlet fermionic
particle, to serve as cold dark matter, and a singlet Higgs are added. We
perform a reanalysis on the free parameters. In particular, demanding a correct
relic abundance of dark matter, we derive and plot the coupling of the singlet
fermion with the singlet Higgs, $g_s$, versus the dark matter mass. We
analytically compute the pair annihilation cross section of singlet fermionic
dark matter into two photons. The thermally averaged of this cross section is
calculated for wide range of energies and plotted versus dark matter mass using
$g_s$ consistent with the relic abundance condition. We also compare our
results with the Fermi-Lat observations.
