Reputation aggregation methods are used in unstructured peer-to-peer (P2P) networks to evaluate the trustworthiness of participating peers and to combat malicious peer's behaviors. In reputation aggregation methods, each peer collects local scores by each transaction and calculates global scores by aggregating local scores. Using the global scores, individual peer can interact with reliable peers. However, existing reputation aggregation methods do not consider the reputation scores of the newly joining peers. In such conditions, file requests concentrate on the existing high reliability peers which leads to download failures. To avoid this problem, NP-Trust distributes the file request to all safe peers including the new peers by providing the newly joining peers with initial files and giving chances to be evaluated. Through computer simulations, the proposed method is compared with Gossip Trust and DFR-Trust in the following criteria: file request variation and transaction success rate. Compared to the DFR-Trust, the proposed method decreased the concentration of the file request by 60% and increased the transaction success rate by 4% and showed that the proposed scheme is efficient in the above two criteria.