The neck growth mechanism of pulse electric current sintering (PECS), especially for non-conductive powder, is a key problem to study. In this paper, the rapid sintering mechanism and local high temperature of the neck at the initial stage in pulse electric current sintering was investigated for non-conductive Al₂O₃ powders based on the L-S (Lord and Shulman) generalized thermoelastic theory. The Comsol Multiphysics was applied to numerically simulate temperature, stress distribution, and the chemical potential and the vacancy concentration of sintering neck. The results show that the heat propagated with a finite velocity, and superposition was produced at sintering neck, so local high temperature generates. The chemical potential on the edge and center of sintering neck shows that surface diffusion is main diffusion mechanism. Local vacancy concentration gradient is present on the sintering neck, promoting the sintering process and reducing the sintering time.