Abstract: The behaviour of electrons in a crystal can be described by Sohrodinger's equation for a periodic potential. Up to now, the transfer matrix technique remains one of the best available to solve problems in one dimension. In this paper, a new matrix method called "the characteristic matrix of periodic potential" is introduced. The traditional transfer matrix connects two amplitudes of plane waves or Bloch waves. Instead, the characteristic matrix simply connecting wave functions and their derivates, makes the evaluation of the elements of characteristic matrix simpler than that of transfer matrix, and makes it more suitable for solving the energy values for complicated potentials in one dimension, especially the periodic potentials.