An exchange bias effect with perpendicular anisotropy is of great interest owing to potential applications such as read heads in magnetic storage devices with high thermal stability and reduced dimensions. Here we report a novel approach for achieving perpendicular exchange bias by orienting the ferromagnetic/antiferromagnetic coupling in the vertical geometry through a unique vertically aligned nanocomposite (VAN) design. Our results demonstrate robust perpendicular exchange bias phenomena in micrometer-thick films employing a prototype material system of antiferromagnetic BiFeO3 and ferromagnetic La0.7Sr0.3MnO3. The unique response of exchange bias to a perpendicular magnetic field reveals the existence of exchange coupling along their vertical heterointerfaces, which exhibits a strong dependence on their strain states. This VAN approach enables a large selection of material systems for achieving perpendicular exchange bias, which could lead to advanced spintronic devices.