Spectral optimization is applied as an effective tool in designing solid-state lighting devices. Optimization speed, however, has been seldomly discussed in previous reports as regards designing an algorithm for white light-emitting diodes (WLEDs). In this study, we propose a method for trichromatic WLEDs to obtain the optimal Ra under target correlated color temperatures (CCTs). Blue-, yellow-, and red-color monochromatic spectra, produced by the GaN LED chip, YAG:Ce3+ phosphors, and CdSe/ZnSe quantum dots, respectively, are adopted to synthesize white light. To improve the effectiveness of our method, the concept of dual weight coefficients is proposed, to maintain a numerical gap between the proposed floating CCT and the target CCT. This gap can effectively guarantee that Ra and CCT ultimately move toward the targeting value simultaneously. Mechanisms of interaction between CCT, Ra, and dual-weight coefficients are investigated and discussed in detail. Particularly, a fitting curve is drawn to reveal the linear relationship between weight coefficients and target CCTs. This finding effectively maintains the accuracy and accelerates the optimization process in comparison with other methods with global searching ability. As an example, we only use 29 iterations to achieve the highest Ra of 96.1 under the target CCT of 4000 K. It is hoped that this study facilitates technology development in illumination-related areas such as residential intelligent lighting and smart planting LED systems.