Abstract: With the first version and second version of quadrilateral area coordinate method (QAC-I and QAC-II) developed, the third version of quadrilateral area coordinate method (QAC-III) is proposed, which, except for retaining main advantages of QAC-I and QAC-II, owns some other distinguishing features. In this paper, QAC-III is used to formulate a new 4-node membrane element with internal parameters, denoted as element QACIII-Q6. This new element exhibits the following advantages: 1) compared with Wilson’s element Q6, this new element possesses high accuracy and is insensitive to mesh distortion. 2) this new element has comparable performance to the Q6 elements formulated by QAC-I and QAC-II, moreover, the procedure in formulation is simple, and the expression for the shape function matrix is concise.