With the aim to get harmonic distortion characteristics and frequency components of modulated output signals of a Mach-Zehnder (MZ) intensity modulator, this paper analyzes the optical intensity modulation transfer function by Tailor expandsion method according with the working principle of modulator. From the viewpoint of spectrum, the output signal is mainly comprised of the fundamental harmonic, the second intermodulation harmonic and the third intermodulation harmonic of the input signal and their magnitudes are connected with the bias voltage and Eigen-phase of MZ modulator. The second harmonic distortion and the fundamental harmonic of the modulated output signal are closely related with the drift of the best bias point. When the modulator works at the best DC bias voltage point, the modulated output signals have the minimum second harmonic distortion. If the best bias point drifts, the second harmonic distortion increases and the fundamental harmonic decreases, which changes in proportion to the sine or cosine of the drift voltage. A 1GHz sine signal with 1V amplitude imposed on the modulator, the simulation results by MATLAB presents that the waveform starts distorting along with the drifting of the best bias voltage, which the fundamental wave component starts decreasing and the second harmonic component starts increasing. While at last the fundamental wave component is zero, the frequency of output modulated signal doubles as much the frequency of input signal.