As implied in the title, the triple-layer remote phosphor (TRP), constructed with the yellow YAG:Ce3+ layer at the bottom, the red CaMgSi2O6:Eu2+,Mn2+ phosphor layer on the top, and the green Ba2Li2Si2O7:Sn2+,Mn2+ phosphor layer between these two layers, is suggested in this paper to improve the color and luminescence of white LEDs (WLEDs). In order to control the red light for the purpose of increasing the color rendering index (CRI), it is suggested that the red CaMgSi2O6:Eu2+,Mn2+ phosphor should be applied in the TRP structure. Simultaneously, the structure uses the green Ba2Li2Si2O7:Sn2+,Mn2+ phosphor layer to control the green light, which increases the luminous efficacy (LE) of WLEDs. In addition, when the concentration of these two phosphors increases, the yellow YAG:Ce3+ concentration must be reduced to keep the average correlated color temperatures (ACCTs) stable at 6000 K to 8500 K. Besides, appropriate adjusting of CRI, LE, and color quality scale (CQS) is also analyzed by modifying the concentration of the green phosphor and red phosphor. The results show that the CRI can get better values if CaMgSi2O6:Eu2+,Mn2+ concentration is higher. In contrast, the CRI decreases dramatically when the concentration of Ba2Li2Si2O7:Sn2+,Mn2+ increases. Meanwhile, CQS can be significantly increased in the range of 10 % to 14 % CaMgSi2O6:Eu2+,Mn2+, regardless of the concentration of Ba2Li2Si2O7:Sn2+,Mn2+. In particular, along with the improvement of CRI and CQS, LE can also be increased by more than 40 % by reducing the scattered light and adding the green light. Obtained results are a valuable reference for manufacturers for improving WLEDs color and luminescence quality to produce a broader range of WLEDs with better quality fulfilling social needs.