It is inevitable and evident that outsourcing complicated intensive tasks to public cloud vendors would be the primary option for resource-constrained clients in order to save cost. Unfortunately, the public cloud vendors are usually untrusted. They may inadvertently leak the data or misuse the user's data, compromise user's privacy or intentionally corrupt computational results to make the system unreliable. It is therefore important how to stop this happening whilst embracing the computational power of public cloud vendors. Non-negative matrix factorization (NMF) is a significant method for conducting data dimension reduction, which has been widely used in large-scale data processing. Nevertheless, due to its non-polynomial hardness, NMF cannot be conducted efficiently using local computation resources, especially when dealing with big data. Motivated by this issue, we address this by presenting a novel outsourced scheme for NMF (O-NMF), which aims to lessen clients' computing burden and tackle secure problems faced by outsourcing NMF. Particularly, based on two non-collusion servers, O-NMF exploits Paillier homomorphism to preserve data privacy. Additionally, O-NMF allows a verification mechanism to assist clients in verifying returned results with high probability. Security analysis and experimental evaluation demonstrates that the validity and practicality of O-NMF is also provided in this work.