  We are interested in the classification of left-invariant symplectic
structures on Lie groups. Some classifications are known, especially in low
dimensions. In this paper we establish a new approach to classify (up to
automorphism and scale) left-invariant symplectic structures on Lie groups. The
procedure is based on the moduli space of left-invariant nondegenerate
$2$-forms. Then we apply our procedure for two particular Lie groups of
dimension $2n$ and give classifications of left-invariant symplectic structures
on them.
