The invention belongs to the field of microwave masers, in particular to a speed-modulated relativistic backward wave tube which operates in a locally inhomogeneous magnetic field. At that same time,the electron beam collection position and the extraction cavity can be ensure to have a certain distance, and the beam wave conversion efficiency can be improved. The structure of the backward wave tube mainly comprises a backward wave tube body, an annular cathode, a first pre-modulation cavity, a second pre-modulation cavity, a resonant reflector, a first section slow wave structure, a modulation cavity, a second section slow wave structure, an extraction cavity, a coaxial collector, an electron beam and a magnetic field coil. A magnetic field coil comprise a first coil and a second coil, and a soft magnetic material ring is arrange between that first coil and the second coil; The first coil, the second coil and the loop of soft magnetic material act together to produce a locally inhomogeneous magnetic field.