We study the dynamical evolution of a two-component Bose-Einstein condensate under a periodic gradient magnetic field. The research methods include analytical analysis in linear regime and numerical simulations in nonlinear regime. In linear regime, the system's wave function, evolving over time, can be analytically solved by applying the rotating wave approximation. The results reveal that the atoms of the two components in the condensate undergo Rabi oscillations under the influence of the magnetic field. By adjusting the gradient and period of the periodic gradient magnetic field, the amplitude and period of the Rabi oscillations can be easily controlled. In the nonlinear regime, we numerically solve the Gross-Pitaevskii equation and find that the results are similar to the linear case when the nonlinearity is weak. However, as the nonlinearity coefficient increases, the resonant points of the system shift, and the proportion of ground state atoms transferred to the excited state gradually decreases. The focus of this study is to, under resonant conditions, transfer ground-state atoms to the excited state through Rabi oscillations. This paves the way for further investigation into the dynamical characteristics of the excited state.