We consider a family of deformations of T-1,T-1 in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T-1,T-1, which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein metric. Next, we consider three-parameter deformations of T-1,T-1 by using classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the ones obtained via TsT transformations, and contain the Lunin-Maldacena background as a special case. It is worth noting that for AdS(5) x T-1,T-1, classical integrability for the full sector has been argued to be lost. Hence our result indicates that the Yang-Baxter sigma model approach is applicable even for non-integrable cosets. This observation suggests that the gravity/CYBE correspondence can be extended beyond integrable cases.