Climate warming and the increased demand in air travels motivate the aviation industry to urgently produce technological innovations. One of the most promising innovations is based on the smoothly continuous morphing leading-edge concept. This study proposes a two-step process for the design of a morphing leading-edge, including the optimization of the outer variable-thickness composite compliant skin and the optimization of the inner kinematic mechanism. For the compliant skin design, an optimization of the variable thickness composite skin is proposed based on a laminate continuity model, with laminate continuity constraint and other manufacturing constraints. The laminate continuity model utilizes a guiding sequence and a ply-drop sequence to describe the overall stacking sequence of plies in different thickness regions of the complaint skin. For the inner kinematic mechanism design, a coupled four-bar linkage system is proposed and optimized to produce specific trajectories at the actuation points on the stringer hats of the compliant skin, which ensures that the compliant skin can be deflected into the aerodynamically optimal profile. Finally, a morphing leading-edge is manufactured and tested. Experimental results are compared with numerical predictions, confirming the feasibility of the morphing leading-edge concept and the overall proposed design approach.