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We have established a caesium double magneto-optical trap (MOT) system for cavity-QED experiment, and demonstrated the continuous transfer of cold caesium atoms from the vapour-cell MOT with a pressure of ～ 1 × 10-6 Pa to the ultra-high-vacuum (UHV) MOT with a pressure of ～ 8 × 10-8 Pa via a focused continuous-wave transfer laser beam. The effect of frequency detuning as well as the intensity of the transfer beam is systematically investigated, which makes the transverse cooling adequate before the atoms leak out of the vapour-cell MOT to reduce divergence of the cold atomic beam. The typical cold atomic flux got from vapour-cell MOT is ～ 2 × 107 atoms/s. About 5 × 106 caesium atoms are recaptured in the UHV MOT.