This paper deals with the finite element method of plane couple stress theory. A discrete Cosserat finite element method is proposed. The displacement and rotation fields are interpolated independently. Kinematic constraints between rotation and displacement gradient are imposed in discrete fashions. A 3-nonded, 9-dof (degree of freedom) triangular discrete Cosserat element (called DCT9) is formulated based on discrete Cosserat technique. Numerical results show that DCT9 element can describe mechanical properties of the Cosserate medium.