A penning trap system called LPT (LANZHOU PENNING TRAP) is now being developed for precise mass measurements in IMP (Institute of Modern Physics). The most key component of LPT is a superconducting magnet. A Phi 156 mm warm bore and two cylinder good field regions with a distance of 220 mm are required for trapping ions and measurements. As the required homogeneity is better than 0.5 ppm, several complicated coaxial coils are used to produce such a magnetic field. The size and position of these coils are optimized by using a method combining linear program with multiobjective optimization. Superconducting shim coils and passive shim pieces are used to eliminate inevitable winding tolerances and environmental influence. The fringe field is decreased to 5 Gs at 2 m line from the center of the magnet by active shielding coils. The designs of the mechanical structure, the quench protection system are also introduced in this paper.