We experimentally demonstrated ultra-fast phase-transparent wavelength conversion using cascaded sum- and difference-frequency generation (cSFG-DFG) in linear-chirped periodically poled lithium niobate (PPLN). Error-free wavelength conversion of a 160-Gb/s return-to-zero differential phase-shift keying (RZ-DPSK) signal was successfully achieved. Thanks to the enhanced conversion bandwidth in the PPLN with linear-chirped periods, no optical equalizer was required to compensate the spectrum distortion after conversion, unlike a previous demonstration of 160-Gb/s RZ on-off keying (OOK) using fixed-period PPLN.