A one-parameter mirror symmetry is a phenomenon of symmetryon a certain pair (X, X') of Calabi-Yau threefolds withh^{2,1}(X)=h^{1,1}(X')=1. Degenerating Hodge structures for a familyof deformations of X play important role in this mirror symmetry. Inthis talk, I will discuss it by using the log Hodge theory and givethe genelic Torelli theorem as an application. This is a joint workwith A. Kanazawa.