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The time-dependent characteristics of the second-harmonic generation of a short pulse are investigated theoretically. Transient coupled-wave equations are necessary to describe the time-dependent process of the second-harmonic generation of a short pulse. It is found that the fundamental waves experience both pulse broadening and compression with different waveform distortion during the frequency-doubling process. The pulse width of a frequency-doubled wave broadens monotonically along the crystal length. There is no phase distortion in the case of exact phase matching. Phase modulation (i.e., chirp) occurs only when there is phase mismatch and chirp can be determined by the phase mismatch.