Cen X-3 is a well-studied high-mass accreting X-ray binary and a variable source of high energy gamma rays from 100 MeV to 1 TeV. The object has been extensively monitored with the University of Durham Mark 6 telescope. Results of observations, including those taken in 1998 and 1999, are reported. There is no evidence for time variability in all the VHE data. There is also no evidence for correlation of the VHE flux with the X-ray flux detected by BATSE and RXTE/ASM. A search for periodic emission, at or close to the X-ray spin period, in the VHE data yielded a 3 sigma upper limit to the pulsed flux of 2.0 x 10^-12 cm^-2 s^-1.