In order to overcome the difficulty of solving nonlinear equations caused by the asymmetry of the past element in present co-rotational approach, the triangular plane elements are studied based on the principle of the combination of co-rotational method and geometric consistency. The origin of the element co-rotation coordinate system is located at the average value point of the three node coordinate values, and coordinate axis directions at the initial time and random calculation time of co-rotational coordinate system are reasonably selected. Based on the principle of virtual work and differentiation, the tangent stiffness matrix of geometric nonlinear element and the corresponding node resistance algorithm of triangular plane element under the condition of large rotation and small strain are established. It shows that the tangent stiffness matrix is symmetric from the calculation formula, and a corresponding program is developed combined with a unified incremental iteration scheme of incremental displacement method and incremental loading method for solving nonlinear equations. The classical examples of flexible column and large deformation cantilever beam are analyzed to verify the correctness of theoretical deduction and the program reliability.