CeNiSn is an interesting heavy fermion compound,with its ground state being a Kondo insulator.The effect of the substitution of Ni by Cu on the specific heat of CeNi1-xCuxSn polycrystal samples is studied through the m ethod of chemical element substitution.A series of samples (x=00,0.02,0.06,0.0 6) were prepared with an electric arc furnace in the atmosphere of flowing high purity argon gas.X-ray powder diffraction analysis shows that all the final samp les have single-phase structure,and that,with the increase of the substitution a mount of Ni,the crystal parameters of the samples become larger.The specific hea t measurements were performed with an adiabatic colorimeter.The results indicate that the doping of Cu increases the specific heat at low temperature,and that t he V-shape gap is gradually suppressed.The physical mechanism may be that the do ping of copper brings about the Kondo lattice discorder and the increase in 3d e lectrons.