The influence of a novel 1,2,4-linking hyperbranched poly(arylenevinylene) (1,2,4-hb-PAV) material, designed to feature intramolecular energy-funneling, on the transport and emission properties of organic light emitting diodes (OLEDs) has been studied. A comparison to conventional hyperbranched 1,3,5-linking polymers (1,3,5-hb-PAV), which do not exhibit this effect, has been made. For this purpose, single-layer organic light emitting diodes with a glass/indium–tin oxide/poly(3,4-ethylenedioxythiophene)/poly(4-styrenesulfonate)/active layer/Ca/Al structure and different active layer thicknesses have been fabricated and characterized, using either 1,2,4-hb-PAV or 1,3,5-hb-PAV as active layers. The current–voltage response has been interpreted in terms of a numerical model that includes a field-dependent carrier mobility, which allows us to estimate carrier mobility in the diodes. Stable green emission with Commission Internationale de L’Eclairage coordinates at (0.41,0.56) and a high luminous efficiency of 28 Cd/A has been obtained at very low driving currents (10 μA) for 1,2,4-hb-PAV material, versus 2.1 Cd/A for the conventional 1,3,5-linking material, in spite of the high photoluminescence quantum yield in thin film exhibited by both materials. The significant improvements in the performance of OLEDs based on 1,2,4-hb-PAV with respect to other conventional hyperbranched polymers are attributed to the inherent energy gradient from the shorter branches to the longer conjugated stem in this structure, which enables the characteristic funneling effect.