Abstract A higher available magnetic field can give more flexibility for significant research and constructions. Inserting feasible high-temperature-superconducting (HTS) magnet inside low-temperature-superconducting (LTS) external is becoming an efficient method to build ultra-high-field (UHF) magnets. However, HTS insert magnets exhibited concentration of magnetic strain during the energization, significantly owing to the screening-current effect. This phenomenon affect the structural integrity of HTS magnets, posing a difficulty for UHF magnets to reach a center field larger than 30 T. In this paper, we report the recent progress of the 35 T all-superconducting UHF magnet project. The full-cycle development of this homemade UHF magnet was a strong collaboration with multiple domestic institutions in China. We used commercial REBa2Cu3O7-x (RE = rare earth element, REBCO) conductors to wind the 20 T HTS insert. Specifically, we optimized the electromagnetic design of this HTS insert with consideration of screening-current induced strain. We applied the no-insulation and metal-as-insulation winding techniques simultaneously to balance the time constant of the two nested REBCO coils. During the excitation test, the HTS insert maintained a 256 A operation current as designed for nearly 18 hours. With the energization of LTS external magnet, the entire facility reached a center field larger than 20 T for 16 hours, 30 T for 6.35 hours and 32 T for 2 hours. It finally reached a 32.4 T center field, at which point the LTS external quenched, inducing the HTS insert to quench as well. After quench, the HTS magnet can maintained 229 A operation current during the postmortem standalone test. This 32.4 T result exhibits effectiveness of considering the screening-current induced strain to enhance the structural integrity of REBCO magnets, and verifies the high reliability of REBCO magnets by generating a long-duration high field environment without any quench accident originating from the REBCO magnet.