  In this paper, we prove the existence of solutions of the Poincar\'e-Lelong
equation $\sqrt{-1}\partial\bar{\partial}u=f$ on a strictly convex bounded
domain $\Omega\subset\mathbb{C}^n$ $(n\geq1)$, where $f$ is a $d$-closed
$(1,1)$ form and is in the weighted Hilbert space
$L^2_{(1,1)}(\Omega,e^{-\varphi})$. The novelty of this paper is to apply a
weighted $L^2$ version of Poincar\'e Lemma for real $2$-forms, and then apply
H\"{o}rmander's $L^2$ solutions for Cauchy-Riemann equations.
