In this paper, we present a new kind of superconducting inductor for a synchronous machine. This inductor is composed of two superconducting coils (solenoids) having the same axis and fed by the same current. A superconducting bulk is used to obtain a variation of the flux density in the air-gap. This superconducting bulk is surrounded by a ferromagnetic material in order to improve the distribution of the radial component of the flux density. With the studied inductor, we obtain a two-pole synchronous machine having a high magnetic field value in the air-gap. The main objective of this paper is to show the feasibility of this new concept of inductor.