We demonstrate a Kerr-lens mode-locked Ti:sapphire laser with an additional Yb(3+) doped Potassium Yttrium Tungstate crystal (Yb:KYW) in the laser cavity, where not only the pump threshold to start mode-locking but also the stable regions to maintain mode-locking can be well-controlled by varying the position of Yb:KYW nearby the confocal focus to change the intracavity Kerr-effects. The pump threshold is reduced down to 800 mW to start the mode-locking operation, which is about 27% less than that for a Ti:sapphire laser without an additional Yb:KYW.