  We construct balanced metrics on the family of non-K\"ahler Calabi-Yau
threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational
curves on K\"ahler Calabi-Yau threefold. As an application, we construct
balanced metrics on complex manifolds diffeomorphic to connected sum of $k\geq
2$ copies of $S^3\times S^3$.
