Curved compound eyes, i.e. microlens arrays on curved surfaces, are highly desirable for their unique optical properties including wide field of view, tracking of fast moving objects and so on. However, it is technically challenging to fabricate biomimetic gapless microlens arrays. In this work, we report a simple method for fabricating close-packed microlenses in a kind of stretchable polymeric material PDMS on curved surfaces inspired by the vertebrate eyes. The successfully fabricated polymeric curved compound eye consists of more than 6000 closepacked ommatidia with an average diameter of 600 mu m for each ommatidium. The ommatidia are located on a convex surface with a diameter of 40mm and thus a total field of view of about 180 degrees has been obtained. The optical test on ommatidia shows that the NA for each ommatidium is about 0.21 and the imaging result of the whole compound eye is also given. Furthermore, an optical relay system is introduced to integrate with the compound eye to form a biomimetic compound eye camera. The formed camera is shown to have a great potential for a broad range of optical imaging applications, such as surveillance imaging, target detection and tracking, surveying and mapping, collision-free navigation of terrestrial and aerospace vehicles.