The influence of a convective structure of the solar photosphere on the shifts of spectral iron lines was studied. Based on the 2-D time-dependent HD solar model atmosphere, we synthesized the line profiles in the visual and infrared spectral ranges. The dependence of the lines shifts on excitation potential, wavelength, and line strength was analyzed in combination with the depression contribution functions. The magnitude of line shifts was found to depend on the difference between the contributions from central parts of granules and from intergranular lanes. Deep in the photosphere the central areas with upflows give the main contribution in the absorption of spatially unresolved weak and moderate lines. The contribution from intergranular lanes is small for these lines. In the upper solar photosphere layers the convective overshooting region is located, and the physical conditions drastically change there. As a result, the line depression contribution from intergranular lanes with downflows grows significantly, while the contributions from the central areas of granules become smaller. This is the reason why blue line shifts decrease and become red, in particular for the strong photospheric lines, which are completely formed in the convective overshootung region. The convective blueshifts observed in infrared lines are smaller than in the visual spectral range because the effective absorption layers are located higher in the photosphere and extend further into the convective overshooting region due to a greater opacity in the infrared range. We also calculated the effective formation depth of visual and infrared synthetic lines, and their dependence on main line parameters is illustrated.