A least square finite element method is employed to solve the time dependent interface advection equation and to calculate the nodal values of the volume fractions (F) in a two phase flow, where the initial values of the volume fractions are determined by an imaginary control volume around each node. Then the quality of the reconstructed interface, which is obtained by the assumption of F=1/2, is evaluated using two different criteria and a highly satisfactory reconstruction is reported, before and after interface advection. Moreover, we benefited from a local least square method to calculate the tangent of the interface at its intersections with the element faces, which is considered to be an important parameter in the surface tension calculations. Finally, some explanatory examples are provided to assess the performance of the introduced method.