In conventional aircrafts, lift control is achieved by using flap systems. It would be beneficial if flap systems could be replaced by a variable-camber morphing wing. It has been shown that variable-camber morphing wings can significantly improve the aerodynamic performance of the aircraft due to the smoothness of the surface, making it possible to fly more efficiently, reduce fuel consumption and reduce the impact on the environment. However, the design of such a variable-camber morphing wing is challenging due to the conflicting requirements of the structure. The wing should be flexible so it can morph, stiff so it can withstand aerodynamic pressures and light weight to reduce fuel consumption. The aim of this work is to provide a method for the density-based topology optimization of compliant morphing structures. The method includes a novel formulation for the objective function which compares the deformed shape of the structure with a desired deformed shape by using a dot product. This method is applied to obtain an optimized design of a compliant variable-camber morphing wing. The obtained design was converted to a prototype by 3D printing and an experiment was performed to assess if the deformed shapes of the prototype were similar to the ones predicted by the analysis in the topology optimization. The experiment showed that for small deformations the output shape matched the predicted output shape. For larger deflections, there was a slight difference. However, the obtained shapes were still quadratic-like and so it is expected that for larger deformations the designed trailing edge will still have superior aerodynamic performance than conventional flap systems.