In traditional methods, the local structure of Petri net is required to compare with all reduction rules. The process is complicate and does not fit for nets with inhibitor arcs. This paper presents a new reduction method. Firstly, Petri net is divided into several maximal acyclic subnets and each one is expressed with logic form. Then, logic algebra is used to reduce the logic form. Finally, the result is reconstructed and embedded in the original net. This paper establishes a method to find and reduce the maximal acyclic subnets and presents the correlative proofs. This method can be applied to Petri nets or subnets with inhibitor arcs and acyclic.