We predict a new class of 3D topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate band gap. Band gap of conventional TI is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands at the Fermi level along with band character inversion occurs in the absence of SOC. Thus large-gap TIs or TIs composed of lighter elements can be expected. In fact, we find by performing first-principles calculations that the model applies to a class of double perovskites A2BiXO6 (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, surface Dirac cones are robust against the presence of dangling bond at boundary.