In this work, a kinetic Monte Carlo (KMC) technique was used to simulate the growth morphology of electrodeposited polycrystalline Ag thin films under a galvanostatic condition (current density). The many-body Embedded Atom Method (EAM) potential has been used to describe the Ag-Ag atomic interaction. Herein, the surface morphology is affected by the kinetic diffusion of adatoms where four jump processes are considered, namely hopping, exchange, step-edge exchange and grain boundary. The results have shown that the surface roughness follows a power law behavior versus film thickness (∝Lα) and time (∝tβ), with the roughness and growth exponents α and β found to be α = 1.14 ± 0.01 and β = 0.57 ± 0.01. The surface morphology under different deposition parameters (current density and substrate temperature) has been discussed in detail. The surface roughness increases where the current density increases due to high deposition rates, which can accelerate the growth of island mode, especially on the (111) surface. In contrast, the surface roughness decreases the temperature of the substrate increases due to thermal agitation, allowing to transform nearly columnar grains to grains with a flat and smooth surface. Finally, the simulations provided information on the subsurface deposition rate of each grain that is not directly available for experimental investigations. It was observed that the (111) grain has a faster deposition rate compared to the (100) and (110) grains due to the low surface energy of the (111) grain.