In this study, we present a new efficient hybrid-mixed composite laminated curved beam element. The present element, which is based on the Hellinger-Reissner variational principle and the first-order shear deformation lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees in order to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the ($6{ imes}6$) element stiffness matrix. The present study also incorporates the straightforward prediction of interlaminar stresses from equilibrium equations. Several numerical examples confirm the superior behavior of the present composite laminated curved beam element.