Net unfoldings are a well-studied partial order semantics for Petri nets. In this paper, we show that the finite prefix of an unfolding, introduced by McMillan, is suited for model checking linear-time temporal properties. The method is based on the so-called automata-theoretic approach to model checking. We propose a technique to treat this approach within the framework of safe Petri nets, and give an efficient algorithm for detecting the system runs violating a given specification.