Single-component white light materials excited by UV have great potential in the field of white LED (WLED) for avoiding the harm of the blue chip and the self-absorption between multi-components. However, the luminous efficiency (LE) of UV-driven WLED based on single-component material is always lower than 15 lm/W. Herein, branched polymers (HPF-PMs and SPF-PMs) with different topology structures (hyperbranched and star-shaped ones) have been synthesized by employing phenylmaleimide (PM) as core unit, and oligomer of fluorene (OF) as arm unit. Both of them exhibit strong yellow emission of PM in neat films with quantum yield up to 92%, due to complete energy transfer (ET) from OF to PM. Interestingly, HPF-PMs and SPF-PMs show dual-emissive white light in silica gel films for incomplete ET. White emission of the composite films can be adjusted by changing loading amount of copolymer, and introducing a green-emissive arylmaleimide core. When the blend films applied in LEDs based on UV chip, highly efficient white electroluminescence with the LE of 16–48 lm/W, and CIE close to (0.33, 0.33) can be realized through down-conversion.