3D Rashba materials can be a leading player in spin-related novel phenomena, ranging from the metallic extreme (unconventional superconductivity) to the transport intermediate (spin Hall effects) to the novel insulating variant (3D topological insulating states). As the essential backbone for both fundamental and applied research of such a 3D Rashba material, this study established the growth of sizeable single crystals of a candidate compound BiTeI with adjusted carrier concentrations. Three techniques (standard vertical Bridgman, modified horizontal Bridgman, and vapour transport) were employed, and BiTeI crystals (>1 × 1 × 0.2 mm(3)) with fundamentally different electronic states from metallic to insulating were successfully grown by the chosen technique. The 3D Rashba electronic states, including the Fermi surface topology, for the corresponding carrier concentrations of the obtained BiTeI crystals were revealed by relativistic first-principles calculations.