We investigate ultra-broadband wavelength converters based on cascaded second-harmonic generation and difference frequency generation using Bessel-chirped gratings (BCGs) in lithium niobate waveguides, and compare them to the ones using uniform grating and segmented grating, respectively. For the same length and power, the BCGs show broader bandwidth than the other two types of grating. The ripple of the matching response is very small as well. Analysis also shows that almost the same conversion bandwidth and maximum conversion efficiency with tolerant response flatness can be achieved when the manufacturing tolerance of the waveguide length is smaller than 0.1 cm.