We demonstrate that conjugated polymers are able to efficiently host blue and white electrophosphorescence if the conjugated polymer has both high triplet energy level (E-T) and high-lying HOMO energy level. A novel conjugated polymer host (PmPTPA) is developed by attaching triphenylamine unit to poly(m-phenylene) backbone. The poly(m-phenylene) backbone endows PmPTPA an Er as high as 2.65 eV, which is sufficiently high to prevent triplet energy back transfer. The tethering triphenylamine unit leads to the HOMO energy level of -5.35 eV for PmPTPA and facilitates hole injection. As the result, blue phosphorescent polymer light-emitting diodes (PPLEDs) based on PmPTPA exhibit the luminance efficiency of 17.9 cd/A and external quantum efficiency of 9.3%. White PPLEDs with blue, green and red phosphorescent dopants dispersed in PmPTPA show the luminance efficiency of 22.1 cd/A and external quantum efficiency of 10.6%.. For both the blue and white PPLEDs based on the conjugated polymer host PmPTPA, the EL performance are fairly comparable to those of the state-of-the-art nonconjugated polymer host, poly(vinyl carbazole) (PVK). These results indicate that PPLEDs with all emission colors. conjugated polymers are suitable host materials for PPLEDs with all emission colors.