This paper presents a finite volume method based on the weighted essentially non-oscillatory(WENO) scheme to develop a phase field method for simulating two-phase ferrofluid flows. The incompressible Navier-Stokes equations is used to describe fluide flow, the Cahn-Hilliard equation is adopted to capture interfacial motion of two-phase flow, and the Maxwell equation is used to describe external magnetic field distribution. At the same time, adding Kelvin force and surface tension to the fluid flow control equation to achieve the description of interface dynamic behavior by magnetic field. To address the challenges posed by the fourth-order nonlinear diffusion terms, the Cahn-Hilliard equation is decomposed into two Helmholtz equations. The fifth-order WENO scheme is employed to handle the convection term, enhancing computational accuracy and mitigating numerical oscillations. Validation through Zalesak’s disk problem shows that the proposed method achieves higher phase interface capture accuracy compared to existing references, while maintaining performance comparable to high-precision phase field methods. The method is applied to investigate droplet shear deformation, revealing its capability to capture more satellite droplets. Moreover,research on the shear deformation of ferromagnetic fluid droplets under the influence of magnetic fields and with lower capillary numbers indicates that the magnetic interfacial force favors droplet deformation when the external magnetic field direction aligns with the hydrodynamic deformation. Furthermore, increasing the magnetic field intensity leads to droplet splitting. Conversely, when the magnetic field is nearly perpendicular to the deformation direction, a low-intensity field alters the deformation trajectory, while a high intensity magnetic field enforces deformation along the magnetic field direction.