Our experimental results show that the presence of a proper amount of negative group velocity dispersion is essential to multi-pulse operation of a Kerr-lens mode-locked femtosecond laser. We demonstrate that the pulse separations and the number of pulses contained within a cavity round trip are strongly dependent on the initial perturbations. The results allow us to get a better understanding on the influences of the convoluted self-phase modulation and intra-cavity dispersions on the stable multi-pulse oscillation in a Kerr-lens mode-locked femtosecond laser.