Conventional aircraft have hinged surfaces like flaps, slats etc. that introduce gaps in the airfoil profile during transition from one flight phase to another resulting in an increased drag, and thereby giving rise to a host of unwanted issues like noise and vibrations. Morphing has been identified as a viable solution. This study focuses on designing a morphing airfoil using topology optimization. The idea is to use the geometric nonlinearity of structures to design a novel camber morphing mechanism using topology optimization, capable of producing a bi-stable airfoil. A hyperelastic material model is used to characterize the large scale deformation undergone by the structure. Two different design domains are investigated and compared. The first design domain is a modified NACA 0012 airfoil with the leading and trailing edges removed. It is meshed with a structured quadrilateral finite-element mesh. The second design domain is a full NACA 0012 airfoil meshed with an unstructured triangular mesh. The nonlinear structural equilibrium equations are solved using a combination of arc-length and displacement controlled Newton-Raphson analysis. A computationally efficient nonlinear optimization algorithm, the Method of Moving Asymptotes (MMA), is used to solve the optimization problem with a Solid Isoparametric Material Penalization (SIMP) scheme. An adjoint sensitivity formulation has been utilized to evaluate the gradient information required for the optimization. The impact of various optimization and design parameters on the final optimized structure and its characteristics has also been studied. The results obtained confirm that topology optimization can be successfully utilized to design a novel camber morphing mechanism without the disadvantages generally associated with the conventional actuation mechanisms like increased weight, higher maintenance costs and low reliability. The optimized results obtained numerically are then 3-D printed to evaluate their performance characteristics.