High-density ZnO nanorods can be grown on pregrown one-dimensional nanostructures via thermal chemical vapor deposition of Zn at a low temperature of 500 degreesC, producing various heterostructures. We demonstrate it using carbon nanotubes, GaN nanowires, GaP nanowires, SiC nanowires, and SiC core-C shell coaxial nanocables. The diameter of ZnO nanorods is in the range of 80-150 nm, and the maximum length is about 3 mum. The ZnO nanorods align vertically on the walls of ID nanostructures, with a uniform growth direction of [001]. We suggest a vapor-liquid-solid growth mechanism that Zn vapor deposits on the ID nanostructures and produces the outer layers encapsulating the ID nanostructures; the ZnO nanorods are grown out from the outer layers of the nanocable structure. The length and density of ZnO nanorods are controllable by the deposition time. All of these heterostructures exhibit intense UV photoluminescence and cathodoluminescence. The green emission intensity is correlated with the density of the ZnO nanorods.