Two novel fluorene-based copolymers (PFSD and PFMD) containing squaric acid or maleimide unit in the main chain were synthesized in good yields by Suzuki coupling reaction. The resulting polymers possess excellent thermal stability, high electron affinity and high photoluminescence (PL) quantum yields. They can fluoresce in yellow-light range due to either the charge transfer between a fluorene segment and an electron-deficient containing squaric acid/maleimide segment of the polymers or the Forster energy transfer between different polymer chains. The results from PL measurements of the isothermally heated polymer thin films show that the commonly observed aggregate excimer formation in polyfluorenes is very effectively suppressed in these two polymers due to the nonlinear structures of maleimide and squaric acid moieties. Double-layer polymer light-emitting diodes (PLED) were fabricated using the resulting polymers as the emitting layers and Ba or Mg : Ag (V : V= 10 : 1) as cathodes. All the devices show bright yellow emission (562-579 nm) with different maximum external quantum efficiencies (0.006%-1.13%). Compared with the other devices, indium-tin oxide (ITO)/polyethylenedioxythiophene (PEDOT) : polystyrene sulfonic acid (PSS)PFMD/Mg : Ag has the higher maximum external quantum efficiency of 1.13% at 564 cd/m2 with a bias of 8.4 V.