The detector KEDR1 is now under construction at the Institute of Nuclear Physics (Novosibirsk, USSR). This detector will be used in high-energy physics experiments on the storage ring VEPP-4M. The paper describes the KEDR magnetic system that consists of a main superconducting coil, compensating superconducting solenoids and an iron yoke closing the magnetic flux. The main superconducting coil is a one-layer solenoid of 3 m diameter and 3 m length with the inductance of 1.2 H, the effective field 2 T, and the stored energy 42 MJ. The superconducting coil was wound around and soldered to the inner surface of a ringlike helium vessel and is cooled indirectly through a 10 mm stainless steel wall of the vessel. A superconducting flux pump supplies the coil with 8 kA current. The iron yoke provides the required uniformity of the field. The compensating superconducting solenoids have a length of 450 mm, a diameter of 120 mm, and a magnetic field of 6.7 T. The total weight of KEDR is approximately equal to 1000 tons.