Dendritic morphology evolution during zinc electrodeposition is a major roadblock in the development of rechargeable zinc anodes in alkaline zinc batteries. In the present work, we report the use of branched polyethylenimine (PEI, M.W.=800g/mol) as an effective electrolyte additive for suppressing dendrite formation during zinc electrodeposition from typical alkaline electrolytes used in secondary zinc batteries. Dendrite suppression is characterized as a function of the PEI concentration via ‘live’ observation of the dendrite propagation using an in-situ optical microscopy setup. Steady-state and transient electrochemical polarization measurements on a rotating disk electrode, combined with electrochemical quartz crystal microgravimetry and ex-situ scanning electron microscopy, reveal the mechanism by which PEI suppresses dendrites, i.e., PEI adsorption on the zinc surface leading to suppression of the zinc electrodeposition kinetics. Our work presents a comprehensive characterization of the role of polymeric additives, such as PEI, in suppressing dendritic growth during alkaline zinc electrodeposition.