Recently, metal-organic frameworks (MOFs) have demonstrated great potential in photocatalysis and luminosity applications. However, most MOFs are dielectrics with substantial band gaps which limits applications of MOFs in the visible-light region. In this paper, we systematically tune the band gap of paradigm MOF-5 by substituting new atoms for the corner elements (X 4Y), in computer simulations using density functional theory. The new proposed materials are labeled X4Y-MOF-5 (X = Zn, Cd, Be, Mg, Ca, Sr, Ba; Y = O, S, Se, Te). These new materials have band gaps ranging from 1.7 to 3.6 eV. The underlying mechanism of tunability of band gap can be ascribed to the electronic states of chalcogen atoms (O, S, Se, Te) in the X4Y nodes and carbon atoms in the BDC linkers. The substantial tunability of band gap leads to a large absorption range covering the visible spectrum. These proposed new materials may be useful for future applications in visible-light promoted photocatalysis or luminosity. The tunability of other properties such as bulk modulus, chemical bonding, and optical properties were also investigated. These novel materials may also be useful for devices in nanoelectronics or optoelectronics.