A "quasi-conforming" triangular laminated shell element based on a refined first-order shear deformation theory is presented. The Hu-Washizu variational principle, involving strain and displacement fields as variables, with stresses being considered as Lagrange multipliers, is used to develop the laminate composite shell element. Both strains and displacements are discretized in the element, while displacements alone are discretized at the boundary. The inter-element C1 continuity is satisfied a posteriori in a weak form. Due to the importance of rotations and shear deformation in the geometrically non-linear analyses of shells, 7 degrees of freedom per node are chosen, viz. three displacements, two first-derivatives in the in-plane directions of the out-of-plane displacement, and two transverse shear strains at each node. To consider the effect of transverse shear deformation on the global behavior of the laminated composite shell, the Reissner-Mindlin first-order theory, with shear correction factors of Chow and Whitney, is adopted. The transverse shear stresses are obtained through the integration of the 3-D equilibrium equations; and the warping induced by transverse shear is considered in the calculation of the in-plane stresses to improve their accuracy. Numerical examples show that the element has good convergence properties and leads to highly accurate stresses.