The HV electron cooling system designed at the Budker Institute of Nuclear Physics for the NICA collider is the world’s only setup developed for a collider and makes it possible to simultaneously cool two ion beams with an energy up to 4.5 GeV/u using the magnetized electron flow . Due to the fact that the cooling system should be installed at the NICA collider, the distance between the beam axes of cooling channels corresponds to the distance between collider beams and amounts to 320 mm. This became the first factor affecting the entire structure of the electron-cooling system and limits the maximum possible outer radius of longitudinal field coils. The energy-consumption limitation of 500–700 kW  can be considered the other factor, and it directly affects the density of filling the solenoid with the conductor. The design of the central solenoid (cooling solenoid) of the electron-cooling system is described, and it has been developed taking into account the imposed limitations.