A 3D mesoscale finite element modelling approach is developed for efficient simulation of complicated failure modes in ultra high performance fibre reinforced concrete (UHPFRC) with explicit modelling of cohesive fibre-matrix interfaces. To effectively model the nonlinear bond-slip between the fibres and the surrounding mortar, a new type of 3D four-noded cohesive-frictional coupled interface element is developed and implemented as a UEL in ABAQUS. To simulate the wrapping effect of mortar on fibres, a kinematic multiple-point-constraint (kMPC) algorithm is proposed and implemented as a user defined MPC algorithm in ABAQUS. A mesh non-conforming technique is devised to insert the new UELs and define the kMPC pairs, so that the meshes of fibres and UELs do not need to conform with the mortar mesh to avoid difficulties in mesh generation. The mortar matrix is modelled by the continuum damaged plasticity model in ABAQUS. The above modelling approach is firstly validated by a uniaxial compressive test of a 40 mm cube, with the FE model directly converted from a micro CT image. The simulated load-displacement curve and the final failure mode are in good agreement with the test. The same model with different fibre dosages is also simulated under uniaxial tension. The results show that the new modelling approach is capable of capturing all the typical failure modes in UHPFRC, such as fibre breakage, mortar cracking and crushing, and fibre-matrix debonding and slipping.