In the weak segregation limit, we investigate the surface-induced structures in the body-centered-cubic phase of diblock copolymers. Employing the Landau-Brazovskii mean field theory, we obtain the extent of surface-induced region as a function of temperature and surface field strength. At strong surface field strengthes, the lamellar and cylindrical characters are much more profound, and the surface-induced structure persists to a larger extent. A "phase diagram" of surface reconstructions is constructed, which describes the surface-induced structure. These results demonstrate that the coupling between the local average excess polymer concentration and the surface leads to lamella-like and cylinder-like structures close to the surface. Some of our theoretical results are in agreement with relevant experimental results. Our predictions about these interesting surface-induced structures should be observable in experiments under suitable conditions.