The nonlinear propegation of picosecond chirped pulses in the normal dispersionregime of single-mode fibers is considered both analytically and numerically. The resultsshow that downchirped pulses can be compressed owing to normal group-velocitydispersion. The compression depends both on the initial peak power and on the initialfrequency chirp of the input pulses. We also show that self-phase-modulation degradespulse compression and that, as the pulse compresses temporally, it synchronously experiences a spectral narrowing.