We report a molecular dynamics simulation of the vapor deposition of amorphous ice on a cold surface. We compare the obtained structure with neutron scattering data of high and low density amorphous ice formed by pressure induced transformation of crystalline ice. The structure of our vapor deposited ice is intermediate between these two, although closer to high density amorphous ice. Its radial distribution functions resemble the results of a simulation of cluster formation in the gas phase as well as of a recent neutron scattering experiment on vapor deposited amorphous ice. The occurrence of an intermediate structure is also in agreement with a recent electron diffraction study. Structural differences are discussed in terms of the hydrogen-bond network. The amorphous surface layer is deeply fissured, suggesting a high porosity of vapor deposited ice.