Biological locomotion, observed in the flexible wings of birds and insects, bodies and fins of aquatic mammals and fishes, consists of their ability to morph the wings/fins. The morphing capability holds significance in the ability of fishes to swim upstream without spending too much energy and that of birds to glide for extended periods of time. Simplifying the wing or fins to a foil, morphing refers to the ability of the foil to change its camber smoothly, without sharp bends on the foil surface. This allows precise control over flow separation and vortex shedding. Compared to conventional trailing-edge extensions or flaps, used in rudders and elevators in submarines and ships, morphing foils provide better control of thrust and lift characteristics. This study aims at understanding the importance of the morphing of foil combined with a sinusoidal heaving motion on thrust generation. A two-dimensional variational stabilized Petrov-Galerkin moving mesh framework is utilized for modelling the incompressible low Reynolds number flow across the flapping foil. The morphing motion is characterized by the extent of morphing, measured as an angle of deviation from the initial camber, and the point of initiation of morphing on the foil as a percentage of its chord length. The effect of the foil morphing and the heaving motion on the propulsive performance are investigated. The extent of morphing is varied from −30° and 30°, and the point of initiation ranges from 15% to 50% of the chord. The Reynolds and Strouhal numbers for the study are 1100 and 0.2, respectively. The results from the current work can pave the way for enhanced engineering designs in bio-mimetics and give insights on design conditions for optimal thrust performance.