A novel degradable adsorbent for the removal of heavy metal ions from waste water, a hyperbranched aliphatic polyester grafted cellulose (HAPE- Cell), was successfully prepared by the simple one-pot method for the first time. The hyperbranched aliphatic polyester was grafted from the surface hydroxyl groups of natural cotton fibers via the solution polycondensation of the AB(2) monomer, 2, 2-bis( hydroxymethyl) propionic acid ( bis-MPA), with the catalysis of p-toluenesulfonic acid (p-TSA). The HAPE- Cell was characterized by elemental analysis, Fourier transform infrared (FT-IR) spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM). The adsorption properties of the HAPE- Cell towards the heavy metal ions (Cu(II), Hg(II), Zn(II), and Cd(II)) were also preliminarily investigated.