A simple and easy to implement technique for femtosecond pulse characterization is proposed and experimentally verified. It is based on the introduction of a known amount of dispersion (by controlling the number of passes through dispersive material) and subsequent recording of the spectral positions of second harmonic peaks obtained in a non-linear crystal. Such dependence allows for direct retrieval of the pulse spectral phase. The presented pulse characterization method is beneficial especially for broadband pulses, where the second harmonic spectrum exceeds the detection bandwidth of a single spectrometer.