The temperature dependence of resistance in the La2/3Ca1/3Mn1-xCuxO3(x=0 and 0.15) system at temperatures much lower than Curie temperature has been experimentally studied. It is found that a resistance minimum obviously appears in the zero-field R-T curve of the Cu-doped sample. Such a resistance minimum disappears when a magnetic field is applied to the sample. Based on Kondo theory, a quantitative comparison between the theory and the experimental data has been presented. It is shown that the experimental observation can be well understood within the framework of Kondo theory.