Carbon nanotubes (CNTs) have recently been integrated in the most widely used material in the world 'concrete' for improving its mechanical properties and fracture resistance. This paper computationally investigates the pull-out behaviour of a single CNT from cement. The effects of: 1) CNT-cement interfacial shear strength, stiffness, and fracture energy; 2) the cement mechanical properties; 3) CNT's mechanical properties, aspect ratio, and surface area to volume ratio on the pull-out strength from a cement matrix are investigated through simulating the single straight CNT pull-out. A coupled elastic-plastic-damage constitutive model is adopted to simulate the behaviour of the cement matrix, whereas the continuum shell model is used to simulate the elastic behaviour of CNT. The surface-based cohesive behaviour is employed for modelling the interface between CNT and cement matrix. It is shown that CNT pull-out is mainly governed by the interfacial fracture energy, and not the interfacial shear strength.