Uniaxial tension and three-point bending tests are conducted on rock-concrete composite specimens with artificial grooving or natural interfaces to investigate the interface mechanics and fracture properties to establish an interface tension-softening constitutive law between concrete and rock for analyzing fracture failure of rock-concrete structures. Tensile strength, fracture energy and initial fracture toughness of a rock-concrete interface are obtained from experiment. Based on the load-displacement curves measured in the three-point bending test, the energy dissipation at a rock-concrete interface is derived using the modified J-integral method. Further, through enforcing a balance between energy dissipation and energy generated by fictitious cohesive forces acting on the fracture process zone, the tension-softening constitutive law of a rock-concrete interface is established, which takes into account the effects of fracture energy and tensile strength of an interface. For the sake of practical applications, the tension-softening constitutive expression is simplified as a bilinear function. Finally, the crack propagation process of a series of concrete-rock composite beams is simulated numerically based on a nonlinear fracture mechanics theory by introducing a crack propagation criterion. The predicted load vs. crack mouth opening displacement (P-CMOD) curves show a reasonable agreement with the experimental ones, verifying the tension-softening constitutive law for a rock-concrete interface derived in this study.