The Poisson-Nernst-Planck (PNP) system is widely used to model charge transport in many physical and biological problems, for example, semiconductors and ion channels. In this talk, we will introduce a PNP system with singular permanent charges. When the permanent charge distribution is an ensemble of point charges in the domain, we transform the original system into a parabolic-elliptic system with weights. We will show the well-posedness of the system in some weighted Sobolev spaces.