In a parabolic quantum dot (QD), the exciton vacuum state and the exciton ground state may be employed as a two-level quantum system——a qubit. The pure dephaseing due to deformation potential exciton-bulk longitudinal acoustic phonon (LAP) interaction for the exciton qubit is investigated by using the reduce density matrix. The dependence of dephasing factor on time and the confinement length of the QD and temperature is calculated. It is shown that the pure dephasing factor increases quickly with increasing time when time is smaller than 2.5ps, and the dephasing time is of the order of ps. Even at absolute zero temperature, exciton-LAP interaction still causes excitonic dephasing. The pure dephasing factor increases with increasing temperature quickly when temperature is higher than 3K. At the same time, it is found that the confinement length of the QD has important effects on pure dephasing of qubit, the smaller the quantum size, the faster the pure dephasing is. The results show that using appropriate QD size at low temperature and using ultra-fast laser technology can effectively suppress pure dephasing due to exciton-LAP interaction.