A pseudo-Riemannian Lie group $(G,〈\cdot ,\cdot 〉)$ is a connected and simply connected Lie group with a left-invariant pseudo-Riemannian metric of type $(p,q)$. This paper is to study pseudo-Riemannian Lie groups with non-Killing conformal vector fields induced by derivations which is an extension from non-Killing left-invariant conformal vector fields. First we prove that a Riemannian (i.e. type $(n,0)$), Lorentzian (i.e. type $(n-1,1)$) or trans-Lorentzian (i.e. type $(n-2,2)$) Lie group with such a vector field is solvable. Then we construct non-solvable unimodular pseudo-Riemannian Lie groups with such vector fields for any $\min (p,q)\ge 3$. Finally, we give the classification for the Riemannian and Lorentzian cases.

伪黎曼李群 $(G,〈\cdot ,\cdot 〉)$ 是具有左不变伪黎曼度量类型的连通且单连通的李群 $(磷,q)$. 本文研究了由非Killing左不变共形矢量场的推导引起的具有非Killing共形矢量场的伪黎曼李群。首先我们证明黎曼（即类型$(n,0)$), Lorentzian (即类型 $(n-1,1)$) 或 trans-Lorentzian (即类型 $(n-2,2)$) 具有这种矢量场的李群是可解的。然后我们用这样的向量场构造不可解的单模伪黎曼李群$\mathrm{分钟}(磷,q)\ge 3$. 最后，我们给出了黎曼和洛伦兹案例的分类。