In the framework of the new version of the gedanken experiments proposed by Sorce and Wald, we investigate the weak cosmic censorship conjecture (WCCC) for an Einstein-Maxwell-Dilaton-Axion (EMDA) black hole. Our result shows that no violations of WCCC can occur with the increase of the background solution parameters for this near-extremal EMDA black hole when the second order correction of the perturbations is taken into account. Namely, the near-extremal EMDA black hole cannot be over-charged or over-spun.