[Purposes] This paper aims to investigate the crack resistance performance of Buton rock asphalt (BRA)-basalt fiber (BF) composite modified asphalt mixtures. [Methods] Small beam bending and semi-circular bending tests were conducted on 70# matrix asphalt mixture, modified asphalt mixture with 20% BRA, and composite modified asphalt mixture with 4% BF and 20% BRA at 15 ℃ and -10 ℃. Based on fracture mechanics theory, indicators such as the maximum bending strain (εＢ), stress intensity factor (KIC), pre-peak fracture energy (Gf), and crack resistance index (CRI) were calculated to compare and analyze the crack resistance performance of asphalt mixtures, and to evaluate the two crack resistance tests of small beam bending and semi-circular bending. [Findings] The addition of BRA can improve the high-temperature stability of asphalt, and the influence of BRA on the crack resistance performance of asphalt mixtures is temperature-dependent. Additionally, the addition of BRA can improve the crack resistance of asphalt mixtures at medium temperature (15 ℃), but has adverse effects on their crack resistance at low temperature (?10 ℃). In contrast, the BRA-BF composite modified mixture exhibits significantly improved crack resistance performance at both medium and low temperatures, indicating that the viscosity enhancement and reinforcement effects of BF can delay the critical cracking point of asphalt mixtures, and thus improve the bending strength and deformation of asphalt mixtures. [Conclusions] Compared with low-temperature small beam bending tests, semi-circular bending tests have a wider temperature range and more significant differences among test results of different materials. Therefore, the semi-circular bending tests are more advantageous in evaluating the crack resistance performance of asphalt mixtures.