We study the dynamical Casimir-Polder force on a two-level atom with different initial states in the one-dimensional dielectric cavity with output coupling, and obtain the analytical expression of the expectation value of dynamical Casimir-Polder force. Results show that the expectation values of dynamical Casimir-Polder force may be affected by the initial states of the atom. Moreover, the expectation value of Casimir-Polder force may vanish at some special atomic positions by properly selecting the initial state of the system. The effects of different relative dielectric constants and the cavity size on the expectation value of Casimir-Polder force are also discussed.