The atomic dipole squeezing is a very important phenomenon in the interaction between an atom and an optical field,but the atomic dipole squeezing of a three-level atom with an intensity-dependent coupling is seldom reported. By using a full quantum theory,We investigate the time-evolution properties of the atomic dipole squeezing of the degenerate quantum-beat three-level atom intensity-dependently interacting with a single-mode coherent field,and explore effects of splitting of the lower energy levels of the atom,the field intensity and the initial atomic coherence on the atomic dipole squeezing. Our results show that,when the two lower levels of the atom is degenerate,dipole squeezing parameters evolve periodically with time,and the splitting of the lower levels destroy this periodicity and reduce the amount of dipole squeezing. The relationship between the amount of dipole squeezing and the initial coherent field intensity is not monotonous. The initial atomic coherence has a great influence on the dipole squeezing.