The contribution of weakly-magnetized (B ∼ 10 9 G) neutron stars accreting the interstellar medium to the diffuse X-ray emission observed in the Galactic Center is investigated. It is shown that, under rather conservative assumptions about the neutron stars and gas distributions, the accretion luminosity can account for a sizable fraction, possibly most, of the detected X-ray flux in the 2.5-7 keV band. In particular, model results are compared with Granat data and show a general agreement in both the flux energy and radial distributions.