In this work we propose a new 4-node DKMQ24 shell element based on Naghdi-Reissner-Mindlin shell theory with 24 degrees of freedom. This new composite shell element, which is developed from DKMQ plate and shell elements, takes into account shear deformation, coupled bending-membrane energy and warping effects. This element has no spurious mode, passes patch tests for membrane, bending and shear problems. It has also successfully passed standard benchmark tests in the case of thick and thin shells without membrane and shear locking. In this paper, we extend the predictive capabilities of the DKMQ24 shell elements to composite laminated plates and shell structures. Numerical results obtained from DKMQ24 are compared against state-of-the-art shell elements. The results obtained by the proposed element converge more rapidly towards the reference solution.