The efficiency of zinc electrodeposition is of fundamental importance for improving long-term performance of aqueous zinc-ion batteries. In order to improve the efficiency of electrodeposition, as well as morphology and reactivity of the zinc deposit, it is possible to use organic additives in the electrolyte. Here, the effect of branched polyethyleneimine (BPEI) as an electrolyte's additive on morphology and kinetics of zinc electrodeposition in 0.5 M of ZnSO4 solution is investigated. The presence of BPEI changes the morphology of the electrodeposited layer from laminated hexagonal large crystals to compact layer without preferential growth morphology. Moreover, we observe that BPEI adsorption on the surface of the substrate suppresses the kinetics of zinc electrodeposition and decreases the grain growth rate, thus favoring the nucleation over the growth. As a result, BPEI ensures a homogeneous distribution of the current densities and can guarantee uniformity of the deposited layer.