In this paper we present a new policy to improve cache performance. The new algorithm called Cache Replacement Using Re-Reference Interval Prediction With Adaptive Bypassing (RRIPAB) which combines the Re-Reference Interval Prediction(RRIP) with a adaptive bypassing algorithm. RRIP have two advantages. The first one is can move block quickly which can reduce the time of useless blocks stay in the cache. The other one is the new block remains in the cache in a shorter time which can evict new blocks fast and give them the time to train. There also cause a problem that many block will be evicted before it hit. So, adaptive bypassing algorithm is a solution of this problem. We evaluate the RRIPAB by performing a simulation study. The simulation results show that RRIPAB reduces the cache miss count by comparing to the LRU policy, the Dynamic Re-Reference Interval Prediction(DRRIP) and the Dueling Segmented LRU Replacement Algorithm with Adaptive Bypassing about 8.7%, 3.4% and 3.5% in 1M LLC, and about 9.9%,4.4% and 2.2% in 4M LLC.