Abstract: A 9-node co-rotational curved quadrilateral shell element for large displacement and large rotation analysis was presented, where vectorial rotational variables were employed. They are the two smaller components of the mid-surface normal vector at each node, and additive in an incremental solution procedure, thus, taking advantage in updating the tangent stiffness matrix. Different from all other existing co-rotational element formulations, the tangent stiffness matrix of the present element was calculated as the second derivatives of the strain energy or Hellinger-Reissner mixed functional with respect to local nodal variables. Due to the commutativity of all nodal variables in calculating the differentiation, the achieved element tangent stiffness matrix is symmetric. To overcome locking problems, the uniformly reduced integration method was adopted in calculating the internal force vector and the element tangent stiffness matrix, and a stabilized method was employed to avoid the occurrence of spurious zero energy modes. Finally, several elastic shell problems were solved to evaluate the performance of the present element, its reliability, computational efficiency and accuracy are satisfying.