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Fiber polymer has been extensively used to improve the mechanical properties and durability of concrete. However, the studies of the effect of fiber polymer on the dynamic performance of recycled aggregate concrete (RAC) is still very limited. In this study, we prepared two types of RAC formulations: RAC reinforced with basalt fibers (BFs) and RAC reinforced with polypropylene fibers (PPs), and compared the effects of fiber types and contents on the air void content, workability (slump), mechanical properties (compressive and flexural strength), dynamic characteristics (dynamic modulus of elasticity and damping ratio), and chloride resistance of RAC. The experimental results showed that the air void content and slump value decreased with the increase of replacement percentage of RCA and fiber contents. Adding PPs provided a more negative effect on the slump of RAC than BFs. The mixtures containing 0.2% PPs and BFs both obtained the highest flexural strength. The addition of PPs was more effective than BFs in improving the damping ratio of RAC, and the mixtures containing 0.3% PPs and BFs both obtained the highest damping ratio. Compared to the RAC without addition of fiber, the charge passed of specimen with addition of PPs approximately increased by 45%, while the specimen with addition of BFs approximately increased by 30%, when the fiber content was 0.3%. This study demonstrates the potential of using fiber to promote the dynamic properties of RAC.