Let $G$ be a Lie group and let $(\mu,J)$ be a left invariant almost pseudo-Hermitian structure on $G$. It is shown that if $(\mu,J)$ is also nearly pseudo-K\"{a}hler, then the tangent bundle $TG$ (with its natural Lie group structure induced from $G$) admits a left-invariant nearly pseudo-K\"{a}hler structure.