Host materials in the emitting layer play an important role in phosphorescent organic light-emitting diodes (PhOLEDs). Two red-phosphorescent bipolar host materials, 9-phenyl-9'-(4-phenylquinazolin-2-yl)-9H,9′H-3,3′-bicarbazole (BQzB2Cz) and 10-(9-phenyl-9H-carbazol-3-yl)-7-(4-phenylquinazolin-2-yl)-7H-benzo[c]carbazole (BQzB2CzB), composing of carbazole moieties of 9-phenyl-9H,9′H-3,3′-bicarbazole and 10-(9-phenyl-9H-carbazol-3-yl)-7H-benzo[c]carbazole as hole-transporting groups and quinazoline moieties as electron-transporting groups, have been synthesized and characterized. The materials exhibit good thermal stability and suitable triplet-state energy levels, and the red PhOLED prepared from BQzB2Cz and BQzB2CzB showed good performance. The OLED prepared with 3 wt% guest material doped BQzB2CzB showed the optimized performance, with the turn-on voltage of 2.8 V, the maximum brightness of 114000 cd/m2, the maximum current efficiency of 21.60 cd/A, the maximum power efficiency of 24.24 lm/W, and the maximum external quantum efficiency (EQEmax) of 25.11 % (at 132 cd/m2). In addition, an EQEmax of 18.91 % was still achieved at 10,000 cd/m2. The lifetime and efficiency of OLED based on BQzB2CzB is improved compared to those of the OLED based on BQzB2Cz. The results indicate that the strategy of designing bipolar host materials with carbazole moieties as hole-transporting groups and quinazolines as electron-transporting units is a practical approach to realizing high-efficiency and high-brightness OLEDs.