The harmonic and phase distortions in the direct modulation of injection lasers are given theoretically with help of a large signal analysis by a Fourier-series-expansion method. It is shown that the distortions are relatively small when there is no-kink in the I-L curve and the magnitudes of the distortions are inversely proportional to the bias current above threshold and proportional to the photon lifetime in laser cavity. It is also shown that the maximum modulation frequency in the analog-modulation is limited by the phase distortion rather than the amplitude distortion.