Abstract Based on the 1,2-3 double-superposition theory proposed by Li and Liu [Int. J. Numer. Meth. Eng. 1997;40:1197], a new global–local higher-order theory for angle-ply laminated plates is derived. This theory fully satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The number of unknowns of the higher-order theories is independent of the layer numbers of the composite laminate. Based on the higher-order theory, a refined four-noded quadrilateral plate element and a refined three-noded triangular element are presented. The interelement C1 weak-continuity conditions can be satisfied. Numerical results show that in-plane stresses and transverse shear stresses can be accurately computed by the direct constitutive equation approach. In order to obtain transverse normal stresses, the equilibrium equation approach is employed here.