Abstract: A process for preparing a polyurethane prepolymer containing carboxylic group(s), or both carboxylic group(s) and double bond(s), which comprises the steps of 1) preparing a diol or triol monomer having carboxylic group(s), or having both carboxylic group(s) and double bond(s) by performing an addition reaction of at least one acid anhydride(s) which may contain double bond(s), with at least one triol or tetraol derivative(s) containing three or four hydroxyl groups in a molar ratio from 0.5:1 to 2:1; and then 2) reacting the obtained diol or triol monomer, or their mixture with a polyol and a diisocyanate or a diisocyanate polymer to give polyurethane prepolymer having an NCO content of 0.1 to 30%, is disclosed. In addition, a process for preparing a water-stable aqueous polyurethane dispersion by neutralizing, dispersing, and chain extending the polyurethane prepolymer obtained above is provided.