The interface between new and old concrete plays a significant role in reinforced concrete engineering due to its size effect and weak strength. To investigate the size effect of tensile strength in new-to-old concrete, splitting tensile tests and computed tomography (CT) scans on composite specimens were conducted. Specimen size, interface roughness, volume fraction of polyvinyl alcohol fiber and adhesive were considered. The tensile bonding strength initially increases and then decreases with interface roughness and fiber content, while size effect on the strength shows a downward trend before rising. The adhesive notably enhances the tensile bonding strength and weakens its size effect. The interface roughness, polyvinyl alcohol fibers and interface agents influence the size effect by modifying the bonding area, specimen uniformity, and characteristic structure of the interface region. At an interface roughness of 5.5 mm and a polyvinyl alcohol fiber content of 0.5 %, the maximum strength was achieved and the maximum attenuation of size effect occurred. The size effect laws of tensile bonding performance were presented based on the Weibull statistical theory, Bažant energy theory and Carpinteri multi-fractal theory. The experimental values exhibit good consistency with the predictions from the size effect models.