A analytic method for the calculation of the electrical characteristics of semiconducting ceramics is suggested. This paper put forward the concept of effective carrier concentration. Electrical characteristics under extra electric field have been calculated by the method of tilted energy band. The non-linear current-voltage characteristics with different grain sizes has been obtained. The results pointed out that the current-voltage characteristics divide into three regions: Linear region before breakdown field, nonlinear region near breakdown field and upturn region after breakdown field; The grain boundary barrier leads to the strong non-linear characteristics, which has nothing to do with the grain size. With the grain size decreasing, the breakdown field increases. The results are compared with experimental data.