Concrete infrastructure repair remains a formidable challenge. The application of engineering geopolymer composites (EGCs) as a repair material in the field of rapid structural repair can ensure the safety of structural facilities and prolong their service life. However, the interfacial bonding performance of existing concrete with EGCs is still unclear. The purpose of this paper is to explore a kind of EGC with good mechanical properties, and to evaluate the bonding performance of EGCs with existing concrete using a tensile bonding test and single shear bonding test. At the same time, X-ray diffraction (XRD) and Scanning electron microscopy (SEM) were adopted to study the microstructure. The results showed that the bond strength increased with the increase in interface roughness. For polyvinyl alcohol (PVA)-fiber-reinforced EGCs, the bond strength increased with the increase in FA content (0–40%). However, with the change of FA content (20–60%), the bond strength of polyethylene (PE) fiber-reinforced EGCs have little change. The bond strength of PVA-fiber-reinforced EGCs increased with the increase in water–binder ratio (0.30–0.34), while that of PE-fiber-reinforced EGCs decreased. The bond–slip model of EGCs with existing concrete was established based on the test results. XRD studies showed that when the FA content was 20–40%, the content of C-S-H gels was high and the reaction was sufficient. SEM studies showed that when the FA content was 20%, the PE fiber–matrix bonding was weakened to a certain extent, so the ductility of EGC was improved. Besides, with the increase in the water–binder ratio (0.30–0.34), the reaction products of the PE-fiber-reinforced EGC matrix gradually decreased.