Summary: We construct many examples of Lie groups admitting a left-invariant metric of negative Ricci curvature. We study Lie algebras which are semidirect products \({\mathfrak{l}}= ({\mathfrak{a}} \oplus{\mathfrak{u}} ) < \ltimes {\mathfrak{n}}\) and we obtain examples where \({\mathfrak{u}}\) is any semisimple compact real Lie algebra, \({\mathfrak{a}}\) is one-dimensional and \({\mathfrak{n}}\) is a representation of \({\mathfrak{u}}\) which satisfies some conditions. In particular, when \({\mathfrak{u}} = {{\mathfrak{s}}}{{\mathfrak{u}}}(m), {{\mathfrak{s}}}{{\mathfrak{o}}} (m)\) or \({{\mathfrak{s}}}{{\mathfrak{p}}} (m)\) and \({\mathfrak{n}}\) is a representation of \({\mathfrak{u}}\) in some space of homogeneous polynomials, we show that these conditions are indeed satisfied. In the case \({\mathfrak{u}} = {{\mathfrak{s}}}{{\mathfrak{u}}}(2)\) we get a more general construction where \({\mathfrak{n}}\) can be any nilpotent Lie algebra where \({{\mathfrak{s}}}{{\mathfrak{u}}}(2)\) acts by derivations. We also prove a general result in the case when \({\mathfrak{u}}\) is a semisimple Lie algebra of non-compact type.