The phase retrieval algorithm of a frequency-resolved optical gating (FROG) is generalized to handle traces seriously distorted by group delay dispersion and non-uniform phase-matching spectra arising from the nonlinear crystal. In our proof-of-concept experiments, 15 mm thick aperiodically poled lithium niobate was employed in FROG, and successfully reconstructed chirped signal pulses were actually stretched by >5 times inside the crystal. This method is particularly promising in the measurement of weak few-cycle pulses produced by supercontinuum generation in fibers.