Fibre-reinforced polymers have been widely used to strengthen masonry structures which owning to their high strength-weight ratio and good durability. The interfacial strength between masonry substrate and FRP plays an essential role in the structural bearing capacity. Plenty of experiments have revealed that interfacial failure typically occurs within a thin layer of masonry near the bond line. The mortar joint's location in the masonry substrate sample influences the bond strength and failure mode and has not been thoroughly investigated. This work focuses on the effect of mortar joints on the normal bond strength and damage process in the pull-off test. The two-dimensional mesoscale finite element model is set up, and zero thickness cohesive elements (cohesive zone model) are inserted into the inner and interface between different materials. The numerical result shows that the mortar joint in the middle of the masonry substrate sample shows the largest normal bond strength, and next to the groove is the smallest.