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A one-dimensional random nanocrystalline chain model is established. A dc electron-phonon-field conductance model of electron tunnelling transfer is set up, and a new dc conductance formula in one-dimensional nanometre systems is derived. By calculating the dc conductivity, the relationship among the electric field, temperature and conductivity is analysed, and the effect of the crystalline grain size and the distortion of interfacial atoms on the dc conductance is discussed. The result shows that the nanometre system appears the characteristic of negative differential dependence of resistance and temperature at low temperature. The dc conductivity of nanometre systems varies with the change of electric field and trends to rise as the crystalline grain size increases and to decrease as the distorted degree of interfacial atoms increases.