In this paper, the generalized Klein-Gordon oscillator is studied in the framework of Lorentz symmetry violation, and the Nikiforov-Uvarov method is used to analyze the Klein-Gordon oscillator with and without magnetic field. On this basis, we analyze some special cases of Klein-Gordon oscillators with Cornell potential functions in detail. The results show that the wave function and the energy eigenvalues of the generalized Klein-Gordon oscillator obviously depend on the Lorentz symmetry violation effect, and the Cornell potential function also has a non-negligible effect on the Klein-Gordon oscillator.