•Debonding occurred at the matrix–fiber interface.•A global width effect was not observed.•After the onset of debonding friction contributed to the increase of the load.•The effective bond length leff due to bond was estimated to be 255mm.•Cohesive material law and fracture energy were obtained from strain profiles. The results of single-lap shear tests, conducted on specimens with fiber reinforced cementitious matrix (FRCM) composite strips bonded to concrete blocks, are presented in this paper. The FRCM composite was comprised of polyparaphenylene benzobisoxazole (PBO) fibers and polymer-modified cement-based mortar. This study indicates that in PBO FRCM–concrete joints debonding mainly occurs at the matrix–fiber interface. Friction between fiber filaments and between fibers and matrix is observed after the debonding process initiates. The experimental data suggest that a width effect does not exist among the fiber bundles, and an effective bond length can be defined and is approximately 260mm. Axial strain profiles along the bonded length are analyzed to investigate the stress-transfer mechanism at the matrix–fiber interface.