Luminescence properties of the yellow-emitting (Ca2Lu1−xCex)(ScMg)Si3O12 (CLSM:xCe3+x = 0.01–0.15) phosphor are investigated for various Ce3+ concentrations. Different Ce3+ emission sites and energy transfers between them are observed, resulting in a red shift of the emission spectra from 530 to 575 nm with increasing x from 0.01 to 0.15. Combining with blue (460 nm) InGaN LEDs, CLSM:Ce3+ shows excellent performances for phosphor-converted white LEDs with higher color rendering index Ra of 87.4–87.9 and lower color temperature TC of 5034–5814 K, especially for warm pcWLEDs with a high color rendering (Ra > 80) and a low color temperature (TC < 4000 K). Thermal quenching behaviors depending on Ce3+ concentrations and temperatures are discussed.