One of the methods to derive white light from light emitting diodes(LEDs) is the multi-chip white LED technology, which mixes the light from red, green and blue LEDs. Introduced is an optimal algorithm for the spectrum design of the multi-chip white LEDs in this paper. It optimizes the selection of single color LEDs and drive current controlling, so that the multi-chip white LED achieves the target correlated color temperature(CCT), as well as high luminous efficacy and good color rendering. A CCT tunable LED light source with four high-power LEDs is realized based on the above optimal design. Test results show that it maintains satisfactory color rendering and stable luminous efficacy across the whole CCT tuning range. Finally, discussed are the design improvement and the prospect of the future applications of the CCT tunable LED light source.