We have observed the giant radio galaxy Centaurus A and the globular cluster omega Centauri in the TeV energy region using the CANGAROO III stereoscopic system. The system has been in operation since 2004 with an array of four Imaging Atmospheric Cerenkov Telescopes ( IACT) with similar to 100m spacings. The observations were carried out in 2004 March and April. In total, approximately 10 hr of data were obtained for each target. No statistically significant gamma-ray signal has been found above 420 GeV over a wide angular region (a 1 degrees radius from the pointing center), and we derive flux upper limits using the wholefield of view. Implications for the total energy of cosmic rays and the density of the cold dark matter are considered.