The cross-correlation method for temporal characterization is investigated using simulations of the two- color above threshold ionization （ATI） on He induced by a vacuum ultraviolet （VUV） free-electron laser （FEL） in the presence of an infrared （IR） field. Non-linear dependencies of the sideband structure pro- duced in the two-color ATI process are expressed as a function of IR laser intensity by considering the spatial distributions and temporal jitter of both lasers. The temporal properties of the FEL pulse can be characterized accurately using the cross-correlation method at a low IR laser intensity of ~3~101~ W/cm2 but with low cross-correlation signals. When the dynamic range of sidebands is increased to high IR intensity, the accuracy of the cross-correlation method becomes crucially dependent on the actual non- linear index. An approach of determining this index is proposed here to improve the accuracy of temporal characterizations.
