The superconducting magnet for a 40-T hybrid magnet is being developed at the High Magnetic Field Laboratory, Chinese Academy of Sciences. The hybrid magnet consists of a resistive insert and a superconducting outsert providing 29 and 11 T, respectively. The superconducting magnet was designed to be wound with four grades of cable-in-conduit conductors (CICCs). The superconducting coils contain over 5000 kg of Nb3Sn/Cu CICC in seven piece lengths. Three dummy conductors and seven prototype conductors have been successfully fabricated without incident. The conductor design, strand cabling, and conductor fabrication details will be introduced in this paper.