High-performance positively-charged nanofiltration (NF) membranes have a profound significance for water softening. In this work, a novel monomer, tris(3-aminopropyl)amine (TAEA), with one tertiary amine group and three primary amine groups, was blended with trace amounts of piperazine (PIP) in aqueous solution to fabricate a positively-charged NF membrane with tunable performance. As the molecular structures of TAEA and PIP are totally different, the chemical composition and structure of the polyamine selective layer could be tailored via varying the PIP content. The resulting optimal membrane exhibited an excellent water permeability of 10.2 LMH bar−1 and a high rejection of MgCl2 (92.4%), due to the incorporation of TAEA/PIP. In addition, this TAEA NF membrane has a superior long-term stability. Thus, this work provides a facile way to prepare a positively charged membrane with an efficient water softening ability.