Ground-state properties of the one-dimensional spin-Peilers model with Dzyaloshi nskii-Moriya（DM）interaction and Kaplan-Shekhtman-Entin-Wohlman-Aharony（KSEA） interactions are studied by Lanczos numerical method. It is shown that the DM interaction acts against dimerization when the DM interaction is irrelative to dimerization. On the other hand, the DM interaction is favorable for dimerization when DM interaction depends on the dimerization. Otherwise, the KSEA interactio n is always against dimerization. The KSEA interaction affects the contribution of the DM interaction to dimerization, and even offsets the effect of DM interac tion. The dimerization vanishes when DM and KSEA interactions are large enough i n some special cases.