Low-temperature cracking is one of the main distresses of asphalt pavements, which reduces their serviceability and leads to water ingress into lower layers of the pavement. The use of modified asphalt mixtures is a way of preventing low-temperature cracking in cold regions. The main objective of this study was to evaluate the fracture resistance of asphalt mixtures modified with carbon nanotubes (CNTs) at low temperatures under different loading conditions using fracture mechanics concepts. Bending beam rheometer (BBR) tests were performed on the neat binder and binders containing 0·5% and 1·2% CNTs to determine the effect of the modifier on the stiffness and relaxation rate of the asphalt binder at low temperatures. Cracked semi-circular bending specimens were then subjected to a fracture test under different loading conditions, which induced deformation from pure opening of the crack mouth (mode I) to pure in-plane shear of the crack (mode II). The results of the BBR tests indicated that 0·5% and 1·2% CNT reduced the stiffness and increased the creep stiffness rate at low temperatures and, as a result, had a positive effect on low-temperature performance by improving thermal cracking resistance. Based on the fracture test results, the asphalt mixtures with 0·5% and 1·2% CNTs showed higher resistance against crack growth than the unmodified asphalt mixture.