We have carried out a surface x-ray diffraction analysis of the geometric structure of a 13-monolayer-thick Fe film on W(110). The Fe adlayer is characterized by a well-ordered two-dimensional array of misfit dislocations that have a periodicity of 35.84 and 50.76 Å along the [001] and [110] directions, respectively. In the (110) plane the average Fe structure is isotropically strained by +1.2% with respect to (bulk) bcc Fe, corresponding to lattice constants of 2.901 Å along [001] and 4.103 Å along [110]. In the surface normal direction ([110]) we find that the Fe film is also strained by +0.22% (c = 4.062 Å). This corresponds to a slightly laterally distorted bct phase with a = b = 2.887 Å, c = 2.901 Å, and γ= 89.4^°. The intensity distribution along 14 satellite rods was analyzed quantitatively using a sine-wave modulation ansatz for the lateral and vertical displacements of the Fe atoms out of their average positions. We find maximum amplitudes in the order of about 0.7 Å for the normal and lateral modulations, respectively. The modulation amplitudes continuously decrease with distance from the Fe/W(110) interface. The adlayer/substrate registry is characterized by a 37/34 coincidence between the Fe- the W atoms, where the vertical Fe corrugation is directly related to the Fe-adsorption site. The implications of the unexpected strain state of the film for its mechanical stress and magnetic anisotropy are discussed.