In this paper, we establish a one-dimensional random nanocrystalline chain model, we derive a new formula of ac electron-phonon-field conductance for electron tunnelling transfer in one-dimensional nanometre systems. By calculating the ac conductivity, the relationship between the electric field, temperature and conductivity is analysed, and the effect of crystalline grain size and distortion of interfacial atoms on the ac conductance is discussed. A characteristic of negative differential dependence of resistance and temperature in the low-temperature region for a nanometre system is found. The ac conductivity increases linearly with rising frequency of the electric field, and it tends to increase as the crystalline grain size increases and to decrease as the distorted degree of interfacial atoms increases.