The vibration characteristics of variable-stiffness based composite curved beams with general layups are examined using a higher-order beam theory that accounts for three-dimensional structural response features. The variable stiffness is spatially considered in the laminated beam by introducing the curvilinear fibres-based layers. The structural model is here represented by a sine-based shear deformable model considering zig-zag function for improving in-plane response and higher order polynomial for capturing through-thickness stretching effect. The appropriate constitutive relationships for laminated composite curved beam with arbitrary layup producing stiffness coupling effects are deduced from three-dimensional elasticity equations. The beam governing equations are then formed applying Hamilton’s principle and the free vibration features are predicted employing the eigenvalue analysis. The effectiveness of the curved laminated beam element developed here is tested against the available analytical solutions in the literature. A detailed numerical analysis by opting for different structural parameters like curved beam angle, thickness, ply-angle, layup, and beam end condition are made to investigate the vibration characteristics of general layup constant stiffness laminated curved beams and by including additional parameter, curvilinear fibre angle variation from centre-to-edge, for variable stiffness laminates.