Considering that the one-tu map can provide a useful and powerful tool to understand the nonlinear dynamics in a designing storage ring dedicated to synchrotron radiation and in a damping ring used as the pre-injector of linear collider, we first expand the Hamiltonian of a charged particle moving along the insertion device (ID)axis to the fourth-order Taylor series, and then construct a second-order symplectic integrator using the Lie map product for the particle passing through one period of the ID. The one-tu map can be obtained by concatenating the Lie map of the whole ID and the rest part of ring.