Based on the exact solution of the time-dependent Schrodinger equation for two-species Bose-Einstein condensates(BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling,we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2)coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.