Anomalous diffusion is known to occur in many fractal structures. The
distance covered in time t is given by r2! approximately t2/dw with d
(w) not-equal 2. Usually sub-diffusive behaviour with d(w)>2 is found
in fractals. We report a computer simulation study of diffusion on a C
antor-bar like lattice, showing that under certain circumstances, enha
nced diffusion with d(w)<2 may be observed.