CeCu6 is one of heavy fermion materials. The effect of the partly substitution of Cu by Au, Ag, Pd and Pt on the low temperature properties has been intensively studied. In this paper, we study the temperature dependence of resistance of CeCu6-xNix(x=0.00, 0.05, 0.10, 0.15, 0.20) at temperatures below 1K. Experimental result shows that the temperature dependence of resistance changes with increase of doping content x. Below 500mK, the resistance of sample with x≈0.1 has a linear temperature dependence, showing a typical non-Fermi liquid behavior, while other samples behave as Fermi liquid. This means x≈0.1 is the critical doping for this system. In the case of Au substitution of Cu, the critical doping of which is also x=0.1, the ground state of the system is changed from Fermi-liquid to non-fermi liquid and antiferromagnetic ordering by volume expansion. But in the present case, the ground state of Ni doping systems changes from FL to NFL due to the magnetism of Ni.