The HT-7U superconducting tokamak is an advanced steady-state plasma physics experimental device to be built in the Institute of Plasma Physics, the Chinese Academy of Sciences (IPP-CAS). The plasma current is 1 MA and the major and minor radius are 1.78 m and 0.4m respectively, with an elongation of 1.85. The preliminary engineering design of the poloidal field (PF) and toroidal field (TF) magnet systems have been done. The PF system is composed of twelve superconducting coils located symmetrically about the equator plane. The central solenoid (CS) assembly is formed by six coils. The TF system consists of 16 superconducting coils. The NbTi cable-in-conduit conductor or (CICC) cooled by a supercritical helium at 4.5 K is chosen as a superconductor for all of the PF and TF coils. At this temperature, the peak magnetic field on the PF magnets is about 4.51 T .The maximum volt-second capacity and the duration of plasma inductive discharge are about 10 Vs and 10 seconds respectively. The stray field in plasma initial region is quite low ( 1.5× 10 -3 T). The magnetic field on the TF magnet is 5.8 T while the toroidal field at the center of the device (R = 1.7 m) is 3.5 T and the ripple of the TF is less than 0.62% at the outer plasma surface (R = 2.1 m). All of the PF and TF magnets are stable during all modes of operation including the plasma disruption. The final design of the PF system is the result of an iterative process involving the use of equilibrium code EQT, magnetic code EFFI, and other codes, which have been developed by our designing group. The HT-7U superconducting tokamak is an advanced steady-state plasma physics experimental device to be built in the Institute of Plasma Physics, the Chinese Academy of Sciences (IPP-CAS). The plasma current is 1 MA and the major and minor radius are 1.78 m and 0.4 m respectively, with an elongation of 1.85. The preliminary engineering design of the poloidal field (PF) and toroidal field (TF) magnet systems have been done. The PF system is composed of twelve superconducting coils located symmetrically about the equator The Central solenoid (CS) assembly is formed by six coils. The TF system consists of 16 superconducting coils. The NbTi cable-in-conduit conductor or (CICC) cooled by a supercritical helium at 4.5 K is chosen as a superconductor for all of the PF and TF coils. At this temperature, the peak magnetic field on the PF magnets is about 4.51 T. The maximum volt-second capacity and the duration of plasma inductive discharges are about 10 Vs and 10 seconds respectively. The magnetic field on the TF magnet is 5.8 T while the toroidal field at the center of the device (R = 1.7 m) is 3.5 T and the ripple of the TF is less than 0.62% at the outer plasma surface (R = 2.1 m). All of the PF and TF magnets are stable during all modes of operation including the plasma disruption. The final design of the PF system is the result of an iterative process involving the use of equilibrium code EQT, magnetic code EFFI, and other codes, which have been developed by our designing group.