Acid-resistant nanofiltration (NF) membranes with both improved permeability and acid stability are in desperate demand for acidic wastewater treatment. Herein, we report a novel polyamine-based nanofiltration membrane with improved flux and excellent acid stability prepared via interfacial cross-linking polymerization reaction of branched polyethyleneimine (BPEI) and 1,4-benzenecarboxylic acid (TPA) with cyanuric chloride (CC) on porous polysulfone support. Evaluated using various characterization techniques, the optimized NF membrane achieved at 1.0% (w/v) BPEI, 0.10% (w/v) CC and 0.15 g/L TPA at 90 °C for 10 min exhibited high rejection of different model salt solutions in the order MgCl₂ > Na₂SO₄ > NaCl, with excellent permeation flux up to 12.8 LMHbar^-1. Furthermore, membrane exhibited good acid stability even at extreme conditions. After exposure to 25% (w/w) H₂SO₄ and 5% (w/w) HNO₃ acid solutions at 25 °C, 55 °C and 80 °C for 720 h, 72 h and 24 h respectively, the fluxes increased with a slight decline in their rejection levels. Meanwhile, a long hour stability test slightly dropped the MgCl₂ rejection level by ～10%. The dynamic CuSO₄/H₂SO₄ mixed solution acid test of the membrane also revealed good permselectivity. This fabricated membrane thus provides a prospect of good application in acidic wastewater treatment and acid recovery process.