A simple method for characterizing the amplitude and phase of picosecond optical pulses from gain-switched laser diodes without autocorrelation measurements is proposed, based on an iterative calculation using only the fundamental and second-harmonic power spectra of an optical pulse to be estimated. The feasibility of the proposed method is examined numerically for gain-switched picosecond pulses obtained using single-mode laser diode rate equations. As a result, although the lack of information normally obtained from autocorrelation measurements means that the initial conditions have a strong influence on the iterative calculation, the proposed method was found to correctly reconstruct the waveform and the frequency-chirp of gain-switched picosecond pulses with an accuracy close to that of the conventional method incorporating autocorrelation measurements.