  A Lie algebra is said to be generalised reductive if it is a direct sum of a
semisimple Lie algebra and a commutative radical. In this paper we extend the
BGG category $\mathcal{O}$ over complex semisimple Lie algebras to the category
$\mathcal {O'}$ over complex generalised reductive Lie algebras. Then we make a
preliminary research on the highest weight modules and the projective modules
in this new category $\mathcal {O'}$, and generalize some conclusions in the
classical case. As a critical difference from the complex semisimple Lie
algebra case, we prove that there is no projective module in $\mathcal {O'}$.
