The propagation and compression of a broad-band pulse in a chirped-pulse-amplification (CPA) laser is studied. Gain narrowing and self-phase-modulation (SPM) are the main mechanisms that modulate the final compressed pulse temporally and spectrally. The effect of gain saturation is also investigated. Due to the large chirp of this type of laser pulse, the power gain of the amplifier can be treated as a function of instantaneous frequency to simplify the analysis. Experimental results from an Nd: glass CPA laser system are in good agreement with the theory. Both experimental and theoretical results show that SPM can play an important role determining the final shape of the compressed pulse, even at relatively low values of the cumulative B-integral, B less than or similar to 2.