The K_S-K_L asymmetries in the D meson decays, induced by the interference between the Cabibbo-favored and the doubly Cabibbo-suppressed amplitudes, can help to understand the dynamics of charm decays. We study the K_S-K_L asymmetries and the branching fractions of corresponding processes in the factorization-assisted topological-amplitude approach in which significant flavor SU(3) symmetry breaking effects are included. Except for the two-body non-leptonic D decays into K_S or K_L and another pseudoscalar meson, we firstly study the K_S-K_L asymmetries in the processes decaying into neutral kaons and a vector meson. The branching fractions of K_L modes are predicted. It is firstly found that the K_S-K_L asymmetries in the D^0 meson decays are shifted by the D^0-D^0bar mixing parameter y_D~0.006, to be 0.113+-0.001 for all the relevant D^0 decay modes. Our results on K_S-K_L asymmetries are consistent with the current data, and could be tested by experiments in the future.