Incorporating reclaimed asphalt pavement (RAP) into asphalt mixtures achieves astonishingly environmental and economic benefits. However, there is hesitation to use higher RAP content due to the concern regarding the deterioration in pavement performance, especially the cracking resistance. Basalt fiber has been considered an effective additive to reinforce the performance of asphalt mixtures and, subsequently, the reinforcement effect is also expected for high-RAP content mixtures. Therefore, this study investigated the effect of basalt fiber on the pavement performance of asphalt mixtures with 0%, 30%, 40%, and 50% RAP contents against high-temperature performance, moisture susceptibility, low-temperature and intermediate-temperature cracking resistance, based on the wheel-tracking test, the uniaxial penetration test, the freeze-thaw splitting test, the low-temperature bending beam test, the semicircular bend fracture test and the indirect tensile asphalt cracking test, respectively. In addition, a performance-space diagram was developed to determine the mixture performance shift caused by basalt fiber. The results showed that adding basalt fiber compensated for the detrimental effect caused by RAP, leading to significant enhancement in moisture susceptibility and low- and intermediate-temperature cracking resistance of mixtures with high RAP content, along with the enhancement in high-temperature performance, indicating that basalt fiber can contribute to the use of high RAP content.