We investigate experimentally the self-compression behavior of high-power femtosecond pulses in normally dispersive solid bulk media with un-chirped laser pulses and negatively chirped laser pulses. It is demonstrated that high-power femtosecond laser pulses can be compressed by the nonlinear propagation in the transparent bulk media, and the temporal and spectral characteristics of resulted pulses were found to be significantly affected by the input laser intensity, with higher intensity corresponding to shorter compressed pulses. By the propagation in a piece of thin BK7 glass plate, a self-compression from 50fs to 20fs was achieved, with a compression factor of about 2.5. However, the output laser pulse was observed to be split into two peaks when the input laser intensity is high enough to generate supercontinuum and conical emission. When the input laser pulse is negatively chirped, the spectra of the pulse is reshaped and narrowed due to strong self-action effects, and the temporal pulse duration is found to be self-compressed, instead of broadening. With the increase in the input pulse intensity, the resulted self-compressed pulses became even shorter than the input laser pulse, and also shorter than sech2 transform-limited pulse according to the corresponding spectra. The self-compression scheme is simple and robust, and it is promising as a new pulse compression method to achieve intense laser pulses of few cycles.