A 9.4 T/400 MHz superconducting magnet with a warm bore of 60 mm is being designed. The 400 MHz NMR magnet is composed of 9 coaxial coils to generate a central field of 9.4 T. The magnetic field homogeneity is better than 4 ppm for 50 mm diameter spherical volume (DSV) and better than 1 ppb for 5 mm DSV. Three types of NbTi strands were used to reduce the cost of the superconducting materials. A preload with 80 MPa was exerted on the superconducting coils and over-banding with stainless steel was adopted to release the stress from the electromagnetic forces. The magnet will be operated in persistent mode with superconducting joints to reduce the field decay. The pulse tube cryocooler with a cooling capacity of 1 W at 4.2 K can be used to reduce the liquid helium evaporation and vibration during operation. The magnet will be equipped with Bi2223/AgAu HTS current leads to reduce the heat losses. In this paper, the design of the 9.4 T NMR superconducting coils, electromagnetic field calculations, and stress analysis of the superconducting coils were presented.