The five-mirror laser cavity containing a semiconductor saturable absorber mirror (SESAM) with negative Kerr effect is theoretically analyzed for the first time. It shows that, compared with the cavity without a SESAM, the upper stable range of the resonator expands obviously after the introduction of SESAM. This indicates that the work point for self-starting can be more close to the edge of the stable range of the CW state, and then get higher nonlinear effect. This shows that the negative Kerr effect of the SESAM can contribute to the self-starting of the modelocked laser besides the saturable absorption mechanism.