Paraconsistent circumscription LPc is a non-classical logic which has both nonmonotonicity and paraconsistency. It can be viewed as a formalism of commonsense reasoning with incomplete and inconsistent knowledge. In this paper, the results of computational complexity on propositional LPc and its implementation algorithm is presented. It is showed that LPc is NP-complete. A linear algorithm to transform LPc into equivalent prioritized circumscription is provided. Because there are a number of useful algorithms for circumscription which could be implemented by resolution, a new way to implementation of LPc is drawn.