  It is well known that a symplectic Lie algebra admit a left symmetric
product. In this work, we study the case where this product is Novikov, we show
that the left-symmetric product associated to the symplectic Lie algrbra is
Novikov if and only if it is associative. In this case the symplectic Lie
algebra is called symplectic Novikov Lie algebra(SNLA). We show that any SNLA
is completely reducible two-step solvable. The classification of
$4$-dimensional and nilpotent $6$-dimensional, also some methods for building
large classes of examples are presented. Finally, we give a geometric study of
the affine connection associated with an SNLA.
