Intense annular electron beam with variable beam radius has important applications in high power microwave (HPM) generation devices with cross-band frequency hopping. This paper proposes a technology of changing the radius of annular electron beam based on the adjustment of the externally guided magnetic field. The core components of the technology include an annular cathode, an anode, an electron beam transfer channel, two transmission channels and an external guide magnet (a three-segment solenoid) system. When the current of the solenoid differs, the solenoid system can generate different magnetic field distributions. In the particle-in-cell (PIC) simulation, when the currents of the three segments are 1 025 A, 107 A, 107 A and 300 A, 300 A, 0 A respectively, the solenoid generates two magnetic fields to achieve the change of the electron beam radius. Based on the theory of single particle motion, this paper deduces the expression of the trajectory of electron beam guided by the gradient magnetic field, explains the principle of the electron beam radius variation under the gradient magnetic field, and investigates the influence of the slope and range of the gradient magnetic field on the electron beam radius. In the cross-band HPM devices simulation, the output power of X-band is 1.6 GW, the frequency is 8.2 GHz, and the power efficiency is 40%. The Ku-band has achieved a power output of 1.5 GW, a frequency of 14.4 GHz, and a power efficiency of 38%.