We present a new paraconsistent approach to logic programming, called Quasi-classical (QC for short) model semantics. The basic idea is the following. We define the QC base as a set of all atoms and their complements, which decouples the link between an atom and its complement at the level of interpretation. Then we define QC models for positive logic programs. The QC model semantics actually effecting on disjunctive programs imposes the link between each disjunction occurring in the head of a rule and its complement disjunct. This enhances the ability of paraconsistent reasoning. We also define weak satisfaction to perform reasoning under our approach. The fixpoint semantics with respect to the QC model semantics is also presented in the paper.