In this paper, we introduce left-invariant (strict) nearly para-Kahler structures on Lie groups (nearly para-Kahler Lie algebras) and present some properties of them. We prove the existence of a unique connection in terms of the characteristic connection on these Lie groups with totally skew- symmetric torsion tensor and we show that the Nijenhuis tensor is parallel with respect to the char- acteristic connection. We determine conditions that allow the curvature tensor of the characteristic connection satis es the rst Bianchi identity. Finally, we focus on anti-abelian almost para-complex structures on Lie groups and we study nearly para-Kahler conditions for these structures. In this study we encounter bi-invariant metrics as pseudo-Riemannian metrics that accept nearly para-Kahler struc- tures. Moreover, we present some examples of nearly para-Kahler Lie algebras.
