The three-dimensional topological insulator is a quantum state of matter characterized by an insulating bulk state and gapless Dirac cone surface states. Device applications of topological insulators require a highly insulating bulk and tunable Dirac carriers, which has so far been difficult to achieve. Here we demonstrate that Bi2-xSbxTe3-ySey is a system that simultaneously satisfies both of these requirements. For a series of compositions presenting bulk-insulating transport behaviour, angle-resolved photoemission spectroscopy reveals that the chemical potential is always located in the bulk band gap, whereas the Dirac cone dispersion changes systematically so that the Dirac point moves up in energy with increasing x, leading to a sign change of the Dirac carriers at x∼0.9. Such a tunable Dirac cone opens a promising pathway to the development of novel devices based on topological insulators.