In the last decade RFID technology has become widespread. It can be found in various fields of our daily life. Due to the rapid development more and more security problems were raised. Since tags have limited memory and very low computational capacity a so-called lightweight authentication is needed. Several protocols have been proposed to resolve security and privacy issues in RFID systems. However, the earlier suggested algorithms do not satisfy all of the security requirements.In this paper we introduce our hash-based mutual authentication protocol which meets all the security requirements. Our solution provides an efficient mutual authentication method. Our protocol can defy the well-known attacks and does not demand high computational capacity.