A new generalized Morse potential function with an additional parameter m is proposed to calculate the cohesive energy of nanoparticles. The calculations showed that a generalized Morse potential function using different values for the m and α parameters can be used to predict experimental values for the cohesive energy of nanoparticles. Moreover, the enlargement of the attractive force in the generalized potential function plays an important role in describing the stability of the nanoparticles rather than the softening of the repulsive interaction in the cases when m > 1.