The ABCD matrix and the general formulae of cavity g parameters are used to analyze and ca!culate the characteristic parameters of a Kerr-lens mode-locking laser. The result shows that KLM strength in the laser is very sensitive to the defocusing distance of the te!escope formed by the two mirrors locating at the two sides of Kerr medium. The mechanism for self-starting operation of Kerr-lens mode-locking laser is studied. Several types of cavity structures with which selfstarting operation of Kerr-lens mode-locking lasers may be achieved are presented. In addition the position of a hard or soft aperture similar as a fast saturable absorber in a KLM laser is discussed.