Abstract: An independent medium surface is introduced to extend the mortar method from a two-field variational principle to a three-field version. The Lagrange multipliers are discretized by using dual basis functions. The dual basis fulfills bi-orthogonal conditions, resulting in the static condensation of the Lagrange multipliers. The dual mortar finite element method using the three-field variational principle is then proposed. This method overcomes the well-known deficiencies of the conventional mortar method, such as the cross-point constraint problem, the master-slave biased problem and the efficiency problem associated with large-scale computations. An in-house code is developed correspondingly and then used to validate the proposed method by two three-dimensional numerical examples. The method achieves high accuracy for interfacial continuous conditions. It can be applied to treat the nonconforming mesh even involving cross-point constraints. The resultant support for the complex subdomain division introduces significant flexibilities to the finite element analysis.