  In this paper, we consider left-invariant para-complex structures on
six-dimensional nilpotent Lie groups. A complete list of six-dimensional
nilpotent Lie groups that admit para-K\"{a}hler structures is obtained,
explicit expressions for para-complex structures are found, and curvature
properties of associated para-K\"{a}hler metrics are investigated. It is shown
that paracomplex structures are nilpotent and the corresponding para-K\"{a}hler
metrics are Ricci-flat.
