The quantum tunnelling of magnetization (QTM) in single crystals of the single molecule magnet (Mn1-xCrx)12-Ac (x=0, 0.03, 0.04, 0.05) has been investigated. In comparison with its parent Mnl2-Ac, a greater rate of magnetization relaxation and a lower effective potential-energy barrier have been observed in Cr-doping samples. This modulation of QTM due to the Cr-doping could be attributed to the small change of Sz due to the smaller spin of Cr itself and additional intrinsic but distributed transverse and longitudinal anisotropy raised by a subtle change of the local environment in the magnetic Mnl2 core.