White organic light-emitting diodes (WOLEDs) have drawn considerable attention for next-generation lighting and display applications owing to their remarkable advantages. Phosphorescent OLED technology is crucial to realize high-efficiency white OLEDs because phosphorescent emitters enable to achieve almost 100% internal quantum efficiency (IQE) by harvesting all the excitons of 75% of triplets and 25% of singlets. However, an efficiency roll-off at high-brightness and a shift in color under various operation biases remains challenges. With the goal towards commercial applications, it requires WOLEDs should simultaneously realize high efficiency at high-brightness region over 1000 cd/m² and good color stability over a wide electroluminescent range. In this paper, we first investigated the energy transfer process between the blue-emitting Bis (3,5-difluoro-2-(2-pyridyl)phenyl-(2-carboxypyridyl) iridium (III) (Firpic) and the orange emitting Iridium (III) bis(4-(4-tert-butylphenyl)thieno3,2-cpyridinato-N,C2')acetylacetonate (PO-01-TB), in addition to the behavior of the carrier trapping in the phosphorescent OLEDs with double emissive layers. Then we successfully fabricated phosphorescent WOLED with multiple emissive layers. The resulting phosphorescent WOLED achieves the maximum forward-viewing current efficiency (CE) of 34.6 cd/A and external quantum efficiency (EQE) of 13.5%, and the CE and the EQE remain 33.9 cd/A and 13.3% at 1000 cd/m², respectively, indicating that the WOLED exhibits low efficiency roll-off. Furthermore, the WOLED shows very stable white emission with small Commission Internationale de L’Eclairage (CIE) coordinate varying range of (0.016, 0.011) from 1000 to 10000 cd/m². The results provide a promising avenue to simultaneously achieve high efficiency, lower the efficiency roll-off at high brightness and color-stability for phosphorescent WOLEDs by carefully designing the device architecture to redistribute the charge carriers and excitons in the recombination zone.