The spreading of a droplet on solid surfaces is important for a wide range of applications, including propulsion, surface coating, spray painting, spray cooling, ink-jet printing and biological sensors. Nowadays computer simulations along with the experimental works have contributions to understand the physical phenomena's. Due to the existing experimental limitations in micro and nano-scales, computational tools assist researchers in understanding the micro and nano phenomena. Molecular dynamics is one of the most accurate tools to simulate the micro and nano scale problems and its use is ever growing. In this study the dynamics of spontaneous and forced spreading of nano-sized droplets on solid surfaces were investigated using molecular dynamics simulations. Interactions between molecules were represented by the Lennard-Jones (LJ) potential. The spreading behavior was analyzed in terms of the temporal evolution of instantaneous spreading diameter and contact angle for surfaces with different wetting characteristics. Also computational model was validated with existing numerical data. The results indicated that the spreading dynamics are mainly governed by surface forces. The spontaneous spreading process on a wettable surface can be described by three different stages, namely the initial, intermediate and final stages. The results indicated that with increasing nano-droplet size and decreasing interaction energy of the surface, contact angle will increase. Also with increasing temperature of system, depending on the interaction energy; the contact angle may increase or decrease. Further the rough surfaces were investigated by using molecular dynamic simulation and contact angle were calculated with changing type of roughness. At last the impacts of nano-droplets were simulated and results indicated that the spreading is influenced by both the magnitude of initial impact velocity and the interaction between the liquid/surface/vapor molecules. All simulations were performed using the LAM software. However, to calculate the contact angle and the spreading diameter, the location of the particles are taken from the LAM output and by separate program, the calculation is done. Keywords : Molecular dynamics simulation, Lennard-Jones potential, nano-droplet, contact angle, spreading diameter