Abstract: The Kelvin-Helmholtz instability (KHI) is one of the hot issues in plasma physics, which has a non-negligible role in space plasma and magnetic confinement fusion. In this paper, a systematic numerical simulation study of the electron-scale KHI in magnetized shear flow is carried out in the relativistic case by using two-dimensional electromagnetic particle simulation method. Emphasis is placed on analyzing the effects of magnetic field direction and strength on the development and nonlinear evolution of the instability. The results show that different external magnetic fields have significant effects on the nonlinear structure of KHI, and perpendicular to the shear plane and the magnetic field pointing to the flow direction as a whole inhibit the development of KHI, whereas no obvious KHI phenomenon is observed in the external magnetic field parallel to the shear plane and perpendicular to the shear velocity, but it will stimulate the nonlinear high-hybrid static plasma oscillations in the direction of the field, and at the same time, the magnetic reconnection and the vortex magnetic island structure are observed in the shear plane. In addition, the energy spectrum of the self-generated magnetic field in the shear plane is derived, and the energy spectrum characteristics are consistent with the spectral power-law distribution presented by the turbulence spectrum.