In nowadays, palladium-catalyzed reactions are of utmost importance in synthetic organic chemistry. Due to advantages of heterogeneous catalysts such as the easy handling and good recyclability, usually these types of catalysts are first choice in constructing a new catalytic system. Here we report a facile approach to prepare hyperbranched polyester-grafted-polyethylene supported palladium nanoparticles as an efficient catalyst in Suzuki reaction and solvent-free aerobic oxidation of alcohols. The reactions were carried out in different conditions with various reagents and the efficiency was determined. Because of the amplification effect of hyperbranched polyester, high loading capacities (around 0.276 mmol g(-1) for Pd) was achieved. The catalyst was characterized with X-ray powder diffraction, scanning electron microscopy, energy-dispersive X-ray spectroscopy, transmission electron microscopy, differential scanning calorimetry and thermogravimetric analysis. This metal nanocatalyst has a very low leaching loss, high activity and selectivity, excellent thermal stability and can be reused at least five times without deactivation of catalytic activity. In this work, a hyperbranched polyester based on 2,2-bis (methylol) propionic acid (bis-MPA) was synthesized and grafted onto carboxylic acid functionalized polyethylene powder. The final nanocatalyst was prepared via solution loading of PdCl2 and reduction to palladium nanoparticles on the HBPE-g-PE. The activity and stability of prepared polymer-supported heterogeneous catalyst was carefully examined for Suzuki reaction and solvent-free oxidation of alcohols.