Femtosecond fiber laser pulse (FFLP) is very suitable for precision laser processing (PLP) with the advantages of high power, compact integrated structure, and easy installation. However, with the power increasing, nonlinear optical effects (NOE) of fiber, such as self-phase modulation (SPM), will be greatly enhanced, and the spectra of the output pulse will be very complex, which considerably increases the temporal complexity of FFLP and takes an immeasurable influence on PLP, so it is of great significance to accurately measure the temporal property of FFLP for higher accuracy of PLP. This paper presents a self-referencing spectral phase interferometry for direct electric-field reconstruction based on a single grating stretcher (SGS-SPIDER) with the two-step phase shift (TSPS) method for measuring FFLP with complex and infrared spectra. Meanwhile, we present a modified pulse-retrieval algorithm called an adaptive pulse-retrieval algorithm (APRA) of frequency-resolved optical gating (FROG) to reconstruct the measured pulse accurately. The duration of the reconstructed pulse measured by FROG is 162 fs, whose autocorrelation curve is similar to the measured autocorrelation curve including the picosecond background. The error of the reconstructed FROG trace is 0.42%, which is reliable enough according to the literature experience. Finally, the unique advantages of FROG for measuring complex ultrashort pulses such as FFLP are compared with SPIDER; that is, FROG has a wider spectral phase measuring range than SPIDER. These studies provide a new diagnostic technique for the complete temporal characterization of FFLP with complex spectra and extend the measurement range and application of SPIDER at the infrared wavelength band, which is significant for improving the accuracy of PLP using FFLP.