Radio frequency identification (RFID) is a technique using radio frequency to object identification and access to relevant data in the open system enviroment with the limits of process, storage, power and so on. The traditional tag authentication protocols taking complicated algorithms into account can't meet the demand. In view of the existing secu-rity and privacy problems of RFID , a lightweight authentication protocol for RFID named LAP was proposed. LAP is based on the generalized inverse matrix and only uses CRC checksum, some matrix and simple logic operations to satisfy the principles of balancing security, privacy and cost. The comparisons of security, privacy and performance with other authentication protocols show that LAP is feasible for RFID tags with requirements of low cost and resource-constrained.