In many fields, multiple RFID tags are often combined into a group to identify an object. An RFID grouping-proof protocol is utilized to prove the simultaneous existence of a group of tags. However, many current grouping-proof protocols cannot simultaneously provide privacy preserving, forward security, and the authentication between reader/verifier and tags, which are vulnerable to trace attack, privacy leakage, and desynchronization attack. To improve the secure performance of the current grouping-proof protocols, we propose two provable lightweight grouping-proof protocols that provide forward security, identity authentication, and privacy preserving. Our protocols involve a trusted reader and an untrusted reader, respectively. In order to avoid verifying some invalid evidences, our protocols complete the authentication of the verifier to the trusted reader and the verified tags before the verifier verifies the grouping-proof evidence. Each tag uses parallel mode to complete its signature to improve the efficiency of the protocols. Moreover, the activate-sleep mechanism and the filtering operation are proposed to effectively reduce the collision probability and computing load of tags. Our protocols complete the authentication to tags twice by a verifier and a trusted reader, respectively. ey can resist various attacks such as eavesdropping, replay, trace, and desynchronization. e protocols are proven to be secure, flexible, and efficient. ey only utilize some lightweight operations. erefore, they are very suitable to the low-cost RFID systems.