A superconducting magnet consisting of REBCO, Nb 3 Sn, and NbTi coils is designed and fabricated at IEE, CAS. There will be a large ac loss generated in the REBCO coil while the magnet is energized. The effect of low temperature background coil size on the ac loss generated in the HTS insert coil is studied. A slab model based on Bean model is adopted to estimate the ac loss in the HTS insert coil. To improve the calculation accuracy, the magnitude and orientation of the magnetic field dependency of I c is introduced in the simulation. The results show that a thinner and higher background magnet will reduce the ac loss in the HTS coil.