We have experimentally demonstrated the self-compression of gegawatt high power femtosecond laser pulses in normally dispersive solid bulk media. It was proved that high-power femtosecond laser pulses can be compressed during the self-focusing propagation in the transparent nonlinear medium. The self-compression behavior was investigated in detail under a variety of experimental conditions, and the temporal and spectral characteristics of resulted pulses are found to be significantly affected by the input pulse intensity, with higher intensity corresponding to shorter compressed pulse. However, the output pulse is split into two peaks when the input intensity is high enough to lead to supercontinuum and conical emission. By the propagation in a piece of BK7 glass, a self-compression from 50fs to 20fs is achieved, with a compression factor of about 2.5. Moreover, we find that pulse self-compression can be achieved with a divergent input laser beam into the glass.