In this paper, a spectral optimization method for a mixed white light-emitting diode (LED) cluster comprising a red/green/blue/cyan/yellow/warm white (R/G/B/C/Y/WW) LED based on pulse width modulation (PWM) is proposed. Following the principle of the spectral combination of multicolor LEDs, the proposed method adopts the 1931 CIE-XYZ tristimulus value to determine the relationship between the color coordinates and the contribution ratio ρ_G+WW(r₁),ρ_B+C(r₂),ρ_R+Y(r₃) for each component, i.e., G+WW,B+C,and R+Y, respectively. Using an optimized traversal range under different flux contribution ratios, i.e., r₁,r₂,and r₃, a maximum color rendering index (R_a) of 96.4, 97.0, 97.3, and 97.4 is attainable when the correlation color temperatures (T_c) of the synthesized white LED cluster are 2700, 4000, 5500, and 7000 K, respectively. Furthermore, experimental verification was conducted with R/G/B/C/Y/WW LEDs. Results show that an R/G/B/C/Y/WW LED module can realize tunable white light in a wide range of T_c (2700--7000 K). When the luminance flux is set to 500 lm, the maximum relative errors of T_c and R_a are 1.96% and 1.24%, respectively, and the luminous efficiency varies in the range 146.81--152.40 lm·W ^-1.