Lithium ion conduction through polycrystalline β-eucryptite ($Li_2O\cdotAl_2O_3\cdot2SiO_2$) as lithium ion conducting solid electrolyte has been studied, as a function of electrolyte/electrode interface morphology and temperature by using an ac impedance technique. AC impedance was measured with Au-Pd or Ag blocking electrode at temperature from 400 to 500℃, in frequency ranging from $10^{-3}$ to $10^5$ Hz. It is suggested that the equivalent circuit of this system consists of a series connection of three parallel RC(frequency dependent) elements, each of which represents grain interior, grain boundary and electrolyte/electrode interface. Nyquist plot allowed to distinguish the grain boundary impedance arc from the bulk impedance arc, and the activation energy for lithium ion conduction across the grain boundary was found to be about 136 kJ/mole. Determination of frequency parameter n by varying the interface morphology with fluoric acid revealed that the constant phase element (CPE) was closely related to the morphology of interface in this system. The electrolyte/Au-Pd electrode interface showed a linear Nyquist plot that becomes more steep with increasing temperature. In contrast, the electrolyte/Ag electrode interface exhibited a deviation from linear Nyquist plot. The lower the temperature or the frequency, the higher the deviating from linearity was.