Fibre reinforced concrete (FRC) exhibits complicated failure modes such as fibre breakage, mortar cracking and spalling, fibre-mortar interfacial debonding, which depend on many material properties, geometric dimensions and loading conditions. Most existing numerical models are unable to reproduce the above failure modes that may occur simultaneously or sequentially, mainly due to the difficulty in generating finite element meshes with a large number of randomly-oriented fibres. Herein we develop a discrete-continuum coupled finite element model for FRC capable of effectively simulating all the major failure modes. The continuum damage-plasticity model is used to simulate damage and fracture behaviour of the mortar, while debonding of fibre-mortar interfaces is modelled by nonlinear cohesive interfacial elements. Unique techniques are identified to generate conforming meshes between fibres and the surrounding mortar so that randomly-oriented fibres are easily modelled. The model is validated by simulating single fiber pullout tests with different inclination angles and direct tensile tests of multiple randomly-distributed fibres.